Tatiana pedraza - Academia.edu (original) (raw)

Papers by Tatiana pedraza

Research paper thumbnail of Radical locally finite T-groups

Groups St Andrews 2005

ABSTRACT A group G is a T-group if every subnormal subgroup of G is normal in G. The class of T-g... more ABSTRACT A group G is a T-group if every subnormal subgroup of G is normal in G. The class of T-groups has been well-studied in finite groups. In the paper under review the authors give a very nice survey of results connected to T-groups, but holding in the class cℒ ¯ of radical locally finite groups satisfying min-p for all primes p. The Wielandt subgroup, ω(G), of a group G is the intersection of all normalizers of subnormal subgroups of G and G is precisely a T-group when G=ω(G). The authors state that in the universe cℒ ¯, ω(G) is the intersection of all normalizers of descendant subgroups of G and hence that in cℒ ¯, T-groups are precisely those groups in which every descendant subgroup is normal. They also state that T-groups that are cℒ ¯-groups are metabelian and state a host of other results, which are proved in [A. Ballester-Bolinches, H. Heineken and T. Pedraza, Forum Math. 19, No. 2, 297-306 (2007; Zbl 1136.20022)].

Research paper thumbnail of (1903-5068) Hyperspace of a fuzzy quasi-uniform space

Iranian Journal of Fuzzy Systems, 2019

Research paper thumbnail of Aggregation of Weak Fuzzy Norms

Symmetry, 2021

Aggregation is a mathematical process consisting in the fusion of a set of values into a unique o... more Aggregation is a mathematical process consisting in the fusion of a set of values into a unique one and representing them in some sense. Aggregation functions have demonstrated to be very important in many problems related to the fusion of information. This has resulted in the extended use of these functions not only to combine a family of numbers but also a family of certain mathematical structures such as metrics or norms, in the classical context, or indistinguishability operators or fuzzy metrics in the fuzzy context. In this paper, we study and characterize the functions through which we can obtain a single weak fuzzy (quasi-)norm from an arbitrary family of weak fuzzy (quasi-)norms in two different senses: when each weak fuzzy (quasi-)norm is defined on a possibly different vector space or when all of them are defined on the same vector space. We will show that, contrary to the crisp case, weak fuzzy (quasi-)norm aggregation functions are equivalent to fuzzy (quasi-)metric agg...

Research paper thumbnail of Aggregation of L-Probabilistic Quasi-Uniformities

Mathematics, 2020

The problem of aggregating fuzzy structures, mainly fuzzy binary relations, has deserved a lot of... more The problem of aggregating fuzzy structures, mainly fuzzy binary relations, has deserved a lot of attention in the last years due to its application in several fields. Here, we face the problem of studying which properties must satisfy a function in order to merge an arbitrary family of (bases of) L-probabilistic quasi-uniformities into a single one. These fuzzy structures are special filters of fuzzy binary relations. Hence we first make a complete study of functions between partially-ordered sets that preserve some special sets, such as filters. Afterwards, a complete characterization of those functions aggregating bases of L-probabilistic quasi-uniformities is obtained. In particular, attention is paid to the case L={0,1}, which allows one to obtain results for functions which aggregate crisp quasi-uniformities. Moreover, we provide some examples of our results including one showing that Lowen’s functor ι which transforms a probabilistic quasi-uniformity into a crisp quasi-unifor...

Research paper thumbnail of New Results on the Aggregation of Norms

Mathematics, 2021

It is a natural question if a Cartesian product of objects produces an object of the same type. F... more It is a natural question if a Cartesian product of objects produces an object of the same type. For example, it is well known that a countable Cartesian product of metrizable topological spaces is metrizable. Related to this question, Borsík and Doboš characterized those functions that allow obtaining a metric in the Cartesian product of metric spaces by means of the aggregation of the metrics of each factor space. This question was also studied for norms by Herburt and Moszyńska. This aggregation procedure can be modified in order to construct a metric or a norm on a certain set by means of a family of metrics or norms, respectively. In this paper, we characterize the functions that allow merging an arbitrary collection of (asymmetric) norms defined over a vector space into a single norm (aggregation on sets). We see that these functions are different from those that allow the construction of a norm in a Cartesian product (aggregation on products). Moreover, we study a related topo...

Research paper thumbnail of Aggregation of fuzzy quasi-metrics

Information Sciences, 2020

In the last years fuzzy (quasi-)metrics and indistinguishability operators have been used as a ma... more In the last years fuzzy (quasi-)metrics and indistinguishability operators have been used as a mathematical tool in order to develop appropriate models useful in applied sciences as, for instance, image processing, clustering analysis and multi-criteria decision making. The both aforesaid similarities allow us to fuzzify the crisp notion of equivalence relation when a certain degree of similarity can be only provided between the compared objects. However, the applicability of fuzzy (quasi-)metrics is reduced because the difficulty of generating examples. One technique to generate new fuzzy binary relations is based on merging a collection of them into a new one by means of the use of a function. Inspired, in part, by the preceding fact, this paper is devoted to study which functions allow us to merge a collection of fuzzy (quasi-)metrics into a single one. We present a characterization of such functions in terms of *-triangular triplets and also in terms of isotonicity and *-supmultiplicativity, where * is a t-norm. We also show that this characterization does not depend on the symmetry of the fuzzy quasi-metrics. The same problem for stationary fuzzy (quasi-)metrics is studied and, as a consequence, characterizations of those functions aggregating fuzzy preorders and indistinguishability operators are obtained.

Research paper thumbnail of Convergencia departamental en los periodos de gobierno 1970 – 1995

Research paper thumbnail of Some results in a class of locally finite groups

The authors present results from their papers J. Algebra 221, No. 2, 562-569 (1999; Zbl 0970.2002... more The authors present results from their papers J. Algebra 221, No. 2, 562-569 (1999; Zbl 0970.20022), Forum Math. 16, No. 5, 717-724 (2004; Zbl 1081.20043) and Bull. Aust. Math. Soc. 63, No. 3, 459-466 (2001; Zbl 0980.20021).

Research paper thumbnail of On radical locally finite groups with min-$p$ for all primes <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi></mrow><annotation encoding="application/x-tex">p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">p</span></span></span></span>

In this survey article the authors present without proofs some of their recent work concerning a ... more In this survey article the authors present without proofs some of their recent work concerning a class ℬ of generalized nilpotent groups within the class ℒ of radical locally finite groups with minimum condition on p-subgroups for every prime p. The class ℬ consists of those ℒ-groups in which every proper subgroup has a proper normal closure. Within the class of ℒ-groups the class of ℬ-groups plays a similar role as the class of nilpotent groups does within the class of finite soluble groups. Thus some well-known facts from the theory of finite soluble groups are generalized and a characterization of the injectors associated with the class ℬ is given. A local approach to this class is also discussed and some results about products of finite nilpotent groups are extended to ℒ-groups which are the product of two ℬ-subgroups.

Research paper thumbnail of Infinite groups with many permutable subgroups

Revista Matemática Iberoamericana, 2008

A subgroup H of a group G is said to be permutable in G, if HK = KH for every subgroup K of G. A ... more A subgroup H of a group G is said to be permutable in G, if HK = KH for every subgroup K of G. A result due to Stonehewer asserts that every permutable subgroup is ascendant although the converse is false. In this paper we study some infinite groups whose ascendant subgroups are permutable (AP-groups). We show that the structure of radical hyperfinite AP-groups behave as that of finite soluble groups in which the relation to be a permutable subgroup is transitive (P T-groups).

Research paper thumbnail of A class of generalized supersoluble groups

Publicacions Matemàtiques, 2005

This paper is devoted to the study of groups G in the universe cL of all radical locally finite g... more This paper is devoted to the study of groups G in the universe cL of all radical locally finite groups with min-p for all primes p such that every δ-chief factor of G is either a cyclic group of prime order or a quasicyclic group. We show that within the universe cL this class of groups behaves very much as the class of finite supersoluble groups.

Research paper thumbnail of Groups whose primary subgroups are normal sensitive

Monatshefte für Mathematik, 2013

ABSTRACT A subgroup of a group is said to be normal sensitive in if for every normal subgroup of ... more ABSTRACT A subgroup of a group is said to be normal sensitive in if for every normal subgroup of . In this paper we study locally finite groups whose -subgroups are normal sensitive. We show the connection between these groups and groups in which Sylow permutability is transitive.

Research paper thumbnail of On periodic radical groups in which permutability is a transitive relation

Journal of Pure and Applied Algebra, 2007

A group G is said to be a PT-group if permutability is a transitive relation in the set of all su... more A group G is said to be a PT-group if permutability is a transitive relation in the set of all subgroups of G. Our purpose in this paper is to study PT-groups in the class of periodic radical groups satisfying min-p for all primes p.

Research paper thumbnail of On a Class of Generalized Nilpotent Groups

Journal of Algebra, 2002

We explore the class of generalized nilpotent groups in the universe c of all radical locally fin... more We explore the class of generalized nilpotent groups in the universe c of all radical locally finite groups satisfying min-p for every prime p. We obtain that this class is the natural generalization of the class of finite nilpotent groups from the finite universe to the universe c. Moreover, the structure of-groups is determined explicitly. It is also shown that is a subgroup-closed c-formation and that in every c-group the Fitting subgroup is the unique maximal normal-subgroup.

Research paper thumbnail of Convergence of fuzzy sets with respect to the supremum metric

Fuzzy Sets and Systems, 2014

We characterize the convergence of fuzzy sets in the supremum metric given by the supremum of the... more We characterize the convergence of fuzzy sets in the supremum metric given by the supremum of the Hausdorff distances of the α-cuts of the fuzzy sets. We do it by dividing this metric into its lower and upper quasipseudometric parts. This characterization is given in the more general context with no assumption on the fuzzy sets. Furthermore, motivated from the theory of Convex Analysis, we also provide some results about the behaviour of the convergence in the supremum metric with respect to maximizers.

Research paper thumbnail of On a class of locally finite T-groups

Forum Mathematicum, 2007

Radical locally finite groups with min-p for all primes p in which every descendant subgroup is n... more Radical locally finite groups with min-p for all primes p in which every descendant subgroup is normal are studied in the paper. It turns out that these groups are precisely Tgroups, that is, groups whose subnormal subgroups are normal.

Research paper thumbnail of Local characterizations of infinite groups whose ascendant subgroups are permutable

Forum Mathematicum, 2010

A subgroup H of a group G is said to be permutable in G, if HK = KH for every subgroup K of G. Ev... more A subgroup H of a group G is said to be permutable in G, if HK = KH for every subgroup K of G. Every permutable subgroup is ascendant, but, in general, the converse is far from being true. In this paper we characterize some infinite groups whose ascendant subgroups are permutable in terms of their Sylow structure. 2001 Mathematics Subject Classification: 20F19; 20F22. Recently locally graded groups (not necessarily periodic) with all subgroups pronormal have been classified in [RRV].

Research paper thumbnail of On products of generalized nilpotent groups

Forum Mathematicum, 2004

Page 1. Forum Math. 16 (2004), 717–724 Forum Mathematicum ( de Gruyter 2004 On products of genera... more Page 1. Forum Math. 16 (2004), 717–724 Forum Mathematicum ( de Gruyter 2004 On products of generalized nilpotent groups Adolfo Ballester-Bolinches and Tatiana Pedraza (Communicated by Rüdiger Göbel) Abstract. Our ...

Research paper thumbnail of The Fitting Subgroup and Some Injectors of Radical Locally Finite Groups with min- p for All p

Communications in Algebra, 2003

ABSTRACT This work was intended as an attempt to continue the study of the class ℬ of generalised... more ABSTRACT This work was intended as an attempt to continue the study of the class ℬ of generalised nilpotent groups started in a previous paper. We present some results concerning the Fitting subgroup and the ℬ-injectors of a radical locally finite group satisfying min-p for all p.

Research paper thumbnail of A local approach to a class of locally finite groups

Bulletin of the Australian Mathematical Society, 2003

This paper is devoted to the study of a class of generalised P-nilpotent groups in the universe c... more This paper is devoted to the study of a class of generalised P-nilpotent groups in the universe cℒ̄ of all radical locally finite groups satisfying min-q for every prime q. Some results of finite groups are extended and a characterisation of the injectors associated with this class is given.

Research paper thumbnail of Radical locally finite T-groups

Groups St Andrews 2005

ABSTRACT A group G is a T-group if every subnormal subgroup of G is normal in G. The class of T-g... more ABSTRACT A group G is a T-group if every subnormal subgroup of G is normal in G. The class of T-groups has been well-studied in finite groups. In the paper under review the authors give a very nice survey of results connected to T-groups, but holding in the class cℒ ¯ of radical locally finite groups satisfying min-p for all primes p. The Wielandt subgroup, ω(G), of a group G is the intersection of all normalizers of subnormal subgroups of G and G is precisely a T-group when G=ω(G). The authors state that in the universe cℒ ¯, ω(G) is the intersection of all normalizers of descendant subgroups of G and hence that in cℒ ¯, T-groups are precisely those groups in which every descendant subgroup is normal. They also state that T-groups that are cℒ ¯-groups are metabelian and state a host of other results, which are proved in [A. Ballester-Bolinches, H. Heineken and T. Pedraza, Forum Math. 19, No. 2, 297-306 (2007; Zbl 1136.20022)].

Research paper thumbnail of (1903-5068) Hyperspace of a fuzzy quasi-uniform space

Iranian Journal of Fuzzy Systems, 2019

Research paper thumbnail of Aggregation of Weak Fuzzy Norms

Symmetry, 2021

Aggregation is a mathematical process consisting in the fusion of a set of values into a unique o... more Aggregation is a mathematical process consisting in the fusion of a set of values into a unique one and representing them in some sense. Aggregation functions have demonstrated to be very important in many problems related to the fusion of information. This has resulted in the extended use of these functions not only to combine a family of numbers but also a family of certain mathematical structures such as metrics or norms, in the classical context, or indistinguishability operators or fuzzy metrics in the fuzzy context. In this paper, we study and characterize the functions through which we can obtain a single weak fuzzy (quasi-)norm from an arbitrary family of weak fuzzy (quasi-)norms in two different senses: when each weak fuzzy (quasi-)norm is defined on a possibly different vector space or when all of them are defined on the same vector space. We will show that, contrary to the crisp case, weak fuzzy (quasi-)norm aggregation functions are equivalent to fuzzy (quasi-)metric agg...

Research paper thumbnail of Aggregation of L-Probabilistic Quasi-Uniformities

Mathematics, 2020

The problem of aggregating fuzzy structures, mainly fuzzy binary relations, has deserved a lot of... more The problem of aggregating fuzzy structures, mainly fuzzy binary relations, has deserved a lot of attention in the last years due to its application in several fields. Here, we face the problem of studying which properties must satisfy a function in order to merge an arbitrary family of (bases of) L-probabilistic quasi-uniformities into a single one. These fuzzy structures are special filters of fuzzy binary relations. Hence we first make a complete study of functions between partially-ordered sets that preserve some special sets, such as filters. Afterwards, a complete characterization of those functions aggregating bases of L-probabilistic quasi-uniformities is obtained. In particular, attention is paid to the case L={0,1}, which allows one to obtain results for functions which aggregate crisp quasi-uniformities. Moreover, we provide some examples of our results including one showing that Lowen’s functor ι which transforms a probabilistic quasi-uniformity into a crisp quasi-unifor...

Research paper thumbnail of New Results on the Aggregation of Norms

Mathematics, 2021

It is a natural question if a Cartesian product of objects produces an object of the same type. F... more It is a natural question if a Cartesian product of objects produces an object of the same type. For example, it is well known that a countable Cartesian product of metrizable topological spaces is metrizable. Related to this question, Borsík and Doboš characterized those functions that allow obtaining a metric in the Cartesian product of metric spaces by means of the aggregation of the metrics of each factor space. This question was also studied for norms by Herburt and Moszyńska. This aggregation procedure can be modified in order to construct a metric or a norm on a certain set by means of a family of metrics or norms, respectively. In this paper, we characterize the functions that allow merging an arbitrary collection of (asymmetric) norms defined over a vector space into a single norm (aggregation on sets). We see that these functions are different from those that allow the construction of a norm in a Cartesian product (aggregation on products). Moreover, we study a related topo...

Research paper thumbnail of Aggregation of fuzzy quasi-metrics

Information Sciences, 2020

In the last years fuzzy (quasi-)metrics and indistinguishability operators have been used as a ma... more In the last years fuzzy (quasi-)metrics and indistinguishability operators have been used as a mathematical tool in order to develop appropriate models useful in applied sciences as, for instance, image processing, clustering analysis and multi-criteria decision making. The both aforesaid similarities allow us to fuzzify the crisp notion of equivalence relation when a certain degree of similarity can be only provided between the compared objects. However, the applicability of fuzzy (quasi-)metrics is reduced because the difficulty of generating examples. One technique to generate new fuzzy binary relations is based on merging a collection of them into a new one by means of the use of a function. Inspired, in part, by the preceding fact, this paper is devoted to study which functions allow us to merge a collection of fuzzy (quasi-)metrics into a single one. We present a characterization of such functions in terms of *-triangular triplets and also in terms of isotonicity and *-supmultiplicativity, where * is a t-norm. We also show that this characterization does not depend on the symmetry of the fuzzy quasi-metrics. The same problem for stationary fuzzy (quasi-)metrics is studied and, as a consequence, characterizations of those functions aggregating fuzzy preorders and indistinguishability operators are obtained.

Research paper thumbnail of Convergencia departamental en los periodos de gobierno 1970 – 1995

Research paper thumbnail of Some results in a class of locally finite groups

The authors present results from their papers J. Algebra 221, No. 2, 562-569 (1999; Zbl 0970.2002... more The authors present results from their papers J. Algebra 221, No. 2, 562-569 (1999; Zbl 0970.20022), Forum Math. 16, No. 5, 717-724 (2004; Zbl 1081.20043) and Bull. Aust. Math. Soc. 63, No. 3, 459-466 (2001; Zbl 0980.20021).

Research paper thumbnail of On radical locally finite groups with min-$p$ for all primes <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi></mrow><annotation encoding="application/x-tex">p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">p</span></span></span></span>

In this survey article the authors present without proofs some of their recent work concerning a ... more In this survey article the authors present without proofs some of their recent work concerning a class ℬ of generalized nilpotent groups within the class ℒ of radical locally finite groups with minimum condition on p-subgroups for every prime p. The class ℬ consists of those ℒ-groups in which every proper subgroup has a proper normal closure. Within the class of ℒ-groups the class of ℬ-groups plays a similar role as the class of nilpotent groups does within the class of finite soluble groups. Thus some well-known facts from the theory of finite soluble groups are generalized and a characterization of the injectors associated with the class ℬ is given. A local approach to this class is also discussed and some results about products of finite nilpotent groups are extended to ℒ-groups which are the product of two ℬ-subgroups.

Research paper thumbnail of Infinite groups with many permutable subgroups

Revista Matemática Iberoamericana, 2008

A subgroup H of a group G is said to be permutable in G, if HK = KH for every subgroup K of G. A ... more A subgroup H of a group G is said to be permutable in G, if HK = KH for every subgroup K of G. A result due to Stonehewer asserts that every permutable subgroup is ascendant although the converse is false. In this paper we study some infinite groups whose ascendant subgroups are permutable (AP-groups). We show that the structure of radical hyperfinite AP-groups behave as that of finite soluble groups in which the relation to be a permutable subgroup is transitive (P T-groups).

Research paper thumbnail of A class of generalized supersoluble groups

Publicacions Matemàtiques, 2005

This paper is devoted to the study of groups G in the universe cL of all radical locally finite g... more This paper is devoted to the study of groups G in the universe cL of all radical locally finite groups with min-p for all primes p such that every δ-chief factor of G is either a cyclic group of prime order or a quasicyclic group. We show that within the universe cL this class of groups behaves very much as the class of finite supersoluble groups.

Research paper thumbnail of Groups whose primary subgroups are normal sensitive

Monatshefte für Mathematik, 2013

ABSTRACT A subgroup of a group is said to be normal sensitive in if for every normal subgroup of ... more ABSTRACT A subgroup of a group is said to be normal sensitive in if for every normal subgroup of . In this paper we study locally finite groups whose -subgroups are normal sensitive. We show the connection between these groups and groups in which Sylow permutability is transitive.

Research paper thumbnail of On periodic radical groups in which permutability is a transitive relation

Journal of Pure and Applied Algebra, 2007

A group G is said to be a PT-group if permutability is a transitive relation in the set of all su... more A group G is said to be a PT-group if permutability is a transitive relation in the set of all subgroups of G. Our purpose in this paper is to study PT-groups in the class of periodic radical groups satisfying min-p for all primes p.

Research paper thumbnail of On a Class of Generalized Nilpotent Groups

Journal of Algebra, 2002

We explore the class of generalized nilpotent groups in the universe c of all radical locally fin... more We explore the class of generalized nilpotent groups in the universe c of all radical locally finite groups satisfying min-p for every prime p. We obtain that this class is the natural generalization of the class of finite nilpotent groups from the finite universe to the universe c. Moreover, the structure of-groups is determined explicitly. It is also shown that is a subgroup-closed c-formation and that in every c-group the Fitting subgroup is the unique maximal normal-subgroup.

Research paper thumbnail of Convergence of fuzzy sets with respect to the supremum metric

Fuzzy Sets and Systems, 2014

We characterize the convergence of fuzzy sets in the supremum metric given by the supremum of the... more We characterize the convergence of fuzzy sets in the supremum metric given by the supremum of the Hausdorff distances of the α-cuts of the fuzzy sets. We do it by dividing this metric into its lower and upper quasipseudometric parts. This characterization is given in the more general context with no assumption on the fuzzy sets. Furthermore, motivated from the theory of Convex Analysis, we also provide some results about the behaviour of the convergence in the supremum metric with respect to maximizers.

Research paper thumbnail of On a class of locally finite T-groups

Forum Mathematicum, 2007

Radical locally finite groups with min-p for all primes p in which every descendant subgroup is n... more Radical locally finite groups with min-p for all primes p in which every descendant subgroup is normal are studied in the paper. It turns out that these groups are precisely Tgroups, that is, groups whose subnormal subgroups are normal.

Research paper thumbnail of Local characterizations of infinite groups whose ascendant subgroups are permutable

Forum Mathematicum, 2010

A subgroup H of a group G is said to be permutable in G, if HK = KH for every subgroup K of G. Ev... more A subgroup H of a group G is said to be permutable in G, if HK = KH for every subgroup K of G. Every permutable subgroup is ascendant, but, in general, the converse is far from being true. In this paper we characterize some infinite groups whose ascendant subgroups are permutable in terms of their Sylow structure. 2001 Mathematics Subject Classification: 20F19; 20F22. Recently locally graded groups (not necessarily periodic) with all subgroups pronormal have been classified in [RRV].

Research paper thumbnail of On products of generalized nilpotent groups

Forum Mathematicum, 2004

Page 1. Forum Math. 16 (2004), 717–724 Forum Mathematicum ( de Gruyter 2004 On products of genera... more Page 1. Forum Math. 16 (2004), 717–724 Forum Mathematicum ( de Gruyter 2004 On products of generalized nilpotent groups Adolfo Ballester-Bolinches and Tatiana Pedraza (Communicated by Rüdiger Göbel) Abstract. Our ...

Research paper thumbnail of The Fitting Subgroup and Some Injectors of Radical Locally Finite Groups with min- p for All p

Communications in Algebra, 2003

ABSTRACT This work was intended as an attempt to continue the study of the class ℬ of generalised... more ABSTRACT This work was intended as an attempt to continue the study of the class ℬ of generalised nilpotent groups started in a previous paper. We present some results concerning the Fitting subgroup and the ℬ-injectors of a radical locally finite group satisfying min-p for all p.

Research paper thumbnail of A local approach to a class of locally finite groups

Bulletin of the Australian Mathematical Society, 2003

This paper is devoted to the study of a class of generalised P-nilpotent groups in the universe c... more This paper is devoted to the study of a class of generalised P-nilpotent groups in the universe cℒ̄ of all radical locally finite groups satisfying min-q for every prime q. Some results of finite groups are extended and a characterisation of the injectors associated with this class is given.