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Papers by mj ata

Research paper thumbnail of Semisimplity Condition and Covering Groups by Subgroups

A cover for a group is a collection of proper subgroups whose union is the whole group. A cover i... more A cover for a group is a collection of proper subgroups whose union is the whole group. A cover is irredundant if no proper sub-collection is also a cover and is called maximal if all its members are maximal subgroups. For an integer n > 2, a cover with n members is called an n-cover. A cover C for a group G is called a C n-cover whenever C is an irredundant maximal core-free n-cover for G and in this case we say that G is a C n-group. Let G denote a semisimple C 8-group and {M i |1 ≤ i ≤ 8} be a maximal irredundant 8-cover for G, with core-free intersection D. Also for each i, 1 ≤ i ≤ 8 we assume that |G : M i | = α i such that α 1 ≤ α 2 ≤ α 3 ≤ α 4 ≤ α 5 ≤ α 6 ≤ α 7 ≤ α 8. In this paper we prove that if G be a semisimple C 8-group and α 3 ≤ 6, then every minimal normal subgroups of G isomorphic to Alt 5 or Alt 6 .

Research paper thumbnail of Identification some groups with special subgroups

International Journal of Algebra, 2018

A cover C for a group G is called a C n-cover whenever C is an irredundant maximal core-free n-co... more A cover C for a group G is called a C n-cover whenever C is an irredundant maximal core-free n-cover for G and in this case we say that G is a C n-group. In this paper we prove that the only C 8-group having at least three maximal subgroups with index 3 and four maximal subgroups with index 2 occuring as a subdirect products of three C 2 s and two primitive groups of degree 3, is (isomorphic to) C 2 × C 2 × C 2 × ((C 3 × C 3) C 2) for which D = 1.

Research paper thumbnail of The C8-group having five maximal subgroups of index 3 and three of index 2

International Journal of Algebra, 2018

A cover C for a group G is called a C n-cover whenever C is an irredundant maximal core-free n-co... more A cover C for a group G is called a C n-cover whenever C is an irredundant maximal core-free n-cover for G and in this case we say that G is a C n-group. In this paper we prove that the only C 8-group having five maximal subgroups of index 3 and three of index 2 occuring as a subdirect products of three C 2 s and two primitive groups of degree 3, is (isomorphic to) C 2 × C 2 × ((C 3 × C 3) C 2) for which D = 1.

Research paper thumbnail of Some results on classification of C_8-groups having special maximal subgroups

International Journal of Algebra, 2017

Let G be a group. A set C of proper subgroups of G is called a cover for G if its set-theoretic u... more Let G be a group. A set C of proper subgroups of G is called a cover for G if its set-theoretic union is equal to G. If the size of C is n, we call C an n-cover for the group G. A cover C for a group G is called irredundant if no proper subset of C is a cover for G. A cover C for a group G is called core-free if the intersection D = M ∈C M of C is core-free in G. A cover C for a group G is called maximal if all the members of C are maximal subgroups of G. A cover C for a group G is called a C n-cover whenever C is an irredundant maximal core-free n-cover for G and in this case we say that G is a C n-group. In this paper we give somer results on classification of C 8-groups having special maximal subgroups.

Research paper thumbnail of Investigation of C8-groups by index condition on maximal subgroups

International Journal of Algebra, 2014

Let D denote the intersection of an arbitrary maximal irredundant 8-cover with core-free intersec... more Let D denote the intersection of an arbitrary maximal irredundant 8-cover with core-free intersection. In this paper we investigated C 8groups by index condition on maximal subgroups.

Research paper thumbnail of C8-groups and subdirect product condition

International Journal of Algebra, 2013

In this paper we investigate all subdirect products of some groups that are not C 8-groups.

Research paper thumbnail of Subdirect products and covering groups by subgroups

International Journal of Algebra, 2013

In this paper we classification subdirect products of some groups that are C 8-groups.

Research paper thumbnail of An Extensive Attitude Towards the Axiomatic Set Theory

Int. J. Contemp. Math. Sciences, 2011

A relatively complete and subjective attitude towards the axiomatic set theory which was achieved... more A relatively complete and subjective attitude towards the axiomatic set theory which was achieved by mathematician, such as Cantor-Zermelo and Fraenkel resulted in the presentation of ten Zermelo-Fraenkel axioms and proposed Cantor and Russell , s paradoxes. In this paper we have tried to remove some proposed paradoxes by defining an exclusive set which we call universal set.

Research paper thumbnail of Identification of C_8-groups by central core

International Journal of Algebra, 2017

Let G denotes a semisimple C8-group and {Mi |1 ≤ i ≤ 8} be a maximal irredundant 8-cover for G, w... more Let G denotes a semisimple C8-group and {Mi |1 ≤ i ≤ 8} be a maximal irredundant 8-cover for G, with core-free intersection D = ⋂8 i=1Mi. Also for each i, 1 ≤ i ≤ 8 we assume that |G : Mi| = αi such that α1 ≤ α2 ≤ α3 ≤ α4 ≤ α5 ≤ α6 ≤ α7 ≤ α8. Let G be a Cn-group, we say that G is a core i2-group if (Mi)G ∩ (Mj)G = 1 for 3 ≤ i < j ≤ 8. Also let G be a Cn-group and core i2-group, then we say that N := (M1)G ∩ (M2)G central core of G. In this paper we show that if G be a semisimple C8-group and αl ≤ 4 then G is core i-2 group. Also we give some results for central core of G. Mathematics Subject Classification: 20F99

Research paper thumbnail of Tuples with Property of Cyclicity Criterions

Journal of Mathematical Extension, 2013

In this paper we give conditions under which a tuple of operators satisfying the hypercyclicity, ... more In this paper we give conditions under which a tuple of operators satisfying the hypercyclicity, supercyclicity and cyclicity criterions.

Research paper thumbnail of C8-Groups and Nilpotency Condition

International Journal of Algebra, 2010

A cover for a group is a collection of proper subgroups whose union is the whole group. A cover i... more A cover for a group is a collection of proper subgroups whose union is the whole group. A cover is irredundant if no proper sub-collection is also a cover and is called maximal if all its members are maximal subgroups. For an integer n > 2, a cover with n members is called an n-cover. In this paper we characterize all nilpotent groups have a maximal irredundant 8-cover with core-free intersection.

Research paper thumbnail of Covering Semisimple Groups by Subgroups

International Journal of Algebra, 2011

A cover for a group is a collection of proper subgroups whose union is the whole group. A cover i... more A cover for a group is a collection of proper subgroups whose union is the whole group. A cover is irredundant if no proper sub-collection is also a cover and is called maximal if all its members are maximal subgroups. For an integer n > 2, a cover with n members is called an n-cover. A cover C for a group G is called a C n-cover whenever C is an irredundant maximal core-free n-cover for G and in this case we say that G is a C n-group. Let G denote a semisimple C 8-group and {M i |1 ≤ i ≤ 8} be a maximal irredundant 8-cover for G, with core-free intersection D. Also for each i, 1 ≤ i ≤ 8 we assume that |G : M i | = α i such that α 1 ≤ α 2 ≤ α 3 ≤ α 4 ≤ α 5 ≤ α 6 ≤ α 7 ≤ α 8. In this paper we prove that If G is a C 8-group and α 1 ≤ α 2 ≤ 4 and α 3 = 6 then G is not semisimple.

Research paper thumbnail of The number of C8-groups for some primitive subgroups

International Journal of Algebra, 2014

In this paper we give the number of C 8-groups for some primitive subgroups.

Research paper thumbnail of Groups with a maximal irredundant 6-cover

A cover for a group G is a collection of proper subgroups whose union is the whole group G. A cov... more A cover for a group G is a collection of proper subgroups whose union is the whole group G. A cover is irredundant if no proper sub-collection is also a cover, and is called maximal if all its members are maximal subgroups. For an integer n &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt; 2, a cover with n members is called an n-cover. Also, we denote σ (G) = n

Research paper thumbnail of CHARACTERIZATION OF p-GROUPS WITH A MAXIMAL IRREDUNDANT 8COVER

A group is covered by a collection of subgroups if it is the union of the collection. The cover i... more A group is covered by a collection of subgroups if it is the union of the collection. The cover is irredundant if no proper sub-collection is also a cover. A cover in which all subgroups are maximal is called maximal. In this paper we completely characterize p-groups (p is a prime) with a maximal irredundant 8-cover with core-free intersection.

Research paper thumbnail of Minimal Blocking Sets in PG ( n , 2) and Covering Groups by Subgroups

Communications in Algebra, 2008

In this paper we prove that a set of points B of P G(n, 2) is a minimal blocking set if and only ... more In this paper we prove that a set of points B of P G(n, 2) is a minimal blocking set if and only if B = P G(d, 2) with d odd and B is a set of d + 2 points of P G(d, 2) no d + 1 of them in the same hyperplane. As a corollary to the latter result we show that if G is a finite 2-group and n is a positive integer, then G admits a C n+1 -cover if and only if n is even and G ∼ = (C 2 ) n , where by a Cm-cover for a group H we mean a set C of size m of maximal subgroups of H whose set-theoretic union is the whole H and no proper subset of C has the latter property and the intersection of the maximal subgroups is core-free. Also for all n < 10 we find all pairs (m, p) (m > 0 an integer and p a prime number) for which there is a blocking set B of size n in P G(m, p) such that B = P G(m, p).

Research paper thumbnail of Semisimplity Condition and Covering Groups by Subgroups

A cover for a group is a collection of proper subgroups whose union is the whole group. A cover i... more A cover for a group is a collection of proper subgroups whose union is the whole group. A cover is irredundant if no proper sub-collection is also a cover and is called maximal if all its members are maximal subgroups. For an integer n > 2, a cover with n members is called an n-cover. A cover C for a group G is called a C n-cover whenever C is an irredundant maximal core-free n-cover for G and in this case we say that G is a C n-group. Let G denote a semisimple C 8-group and {M i |1 ≤ i ≤ 8} be a maximal irredundant 8-cover for G, with core-free intersection D. Also for each i, 1 ≤ i ≤ 8 we assume that |G : M i | = α i such that α 1 ≤ α 2 ≤ α 3 ≤ α 4 ≤ α 5 ≤ α 6 ≤ α 7 ≤ α 8. In this paper we prove that if G be a semisimple C 8-group and α 3 ≤ 6, then every minimal normal subgroups of G isomorphic to Alt 5 or Alt 6 .

Research paper thumbnail of Identification some groups with special subgroups

International Journal of Algebra, 2018

A cover C for a group G is called a C n-cover whenever C is an irredundant maximal core-free n-co... more A cover C for a group G is called a C n-cover whenever C is an irredundant maximal core-free n-cover for G and in this case we say that G is a C n-group. In this paper we prove that the only C 8-group having at least three maximal subgroups with index 3 and four maximal subgroups with index 2 occuring as a subdirect products of three C 2 s and two primitive groups of degree 3, is (isomorphic to) C 2 × C 2 × C 2 × ((C 3 × C 3) C 2) for which D = 1.

Research paper thumbnail of The C8-group having five maximal subgroups of index 3 and three of index 2

International Journal of Algebra, 2018

A cover C for a group G is called a C n-cover whenever C is an irredundant maximal core-free n-co... more A cover C for a group G is called a C n-cover whenever C is an irredundant maximal core-free n-cover for G and in this case we say that G is a C n-group. In this paper we prove that the only C 8-group having five maximal subgroups of index 3 and three of index 2 occuring as a subdirect products of three C 2 s and two primitive groups of degree 3, is (isomorphic to) C 2 × C 2 × ((C 3 × C 3) C 2) for which D = 1.

Research paper thumbnail of Some results on classification of C_8-groups having special maximal subgroups

International Journal of Algebra, 2017

Let G be a group. A set C of proper subgroups of G is called a cover for G if its set-theoretic u... more Let G be a group. A set C of proper subgroups of G is called a cover for G if its set-theoretic union is equal to G. If the size of C is n, we call C an n-cover for the group G. A cover C for a group G is called irredundant if no proper subset of C is a cover for G. A cover C for a group G is called core-free if the intersection D = M ∈C M of C is core-free in G. A cover C for a group G is called maximal if all the members of C are maximal subgroups of G. A cover C for a group G is called a C n-cover whenever C is an irredundant maximal core-free n-cover for G and in this case we say that G is a C n-group. In this paper we give somer results on classification of C 8-groups having special maximal subgroups.

Research paper thumbnail of Investigation of C8-groups by index condition on maximal subgroups

International Journal of Algebra, 2014

Let D denote the intersection of an arbitrary maximal irredundant 8-cover with core-free intersec... more Let D denote the intersection of an arbitrary maximal irredundant 8-cover with core-free intersection. In this paper we investigated C 8groups by index condition on maximal subgroups.

Research paper thumbnail of C8-groups and subdirect product condition

International Journal of Algebra, 2013

In this paper we investigate all subdirect products of some groups that are not C 8-groups.

Research paper thumbnail of Subdirect products and covering groups by subgroups

International Journal of Algebra, 2013

In this paper we classification subdirect products of some groups that are C 8-groups.

Research paper thumbnail of An Extensive Attitude Towards the Axiomatic Set Theory

Int. J. Contemp. Math. Sciences, 2011

A relatively complete and subjective attitude towards the axiomatic set theory which was achieved... more A relatively complete and subjective attitude towards the axiomatic set theory which was achieved by mathematician, such as Cantor-Zermelo and Fraenkel resulted in the presentation of ten Zermelo-Fraenkel axioms and proposed Cantor and Russell , s paradoxes. In this paper we have tried to remove some proposed paradoxes by defining an exclusive set which we call universal set.

Research paper thumbnail of Identification of C_8-groups by central core

International Journal of Algebra, 2017

Let G denotes a semisimple C8-group and {Mi |1 ≤ i ≤ 8} be a maximal irredundant 8-cover for G, w... more Let G denotes a semisimple C8-group and {Mi |1 ≤ i ≤ 8} be a maximal irredundant 8-cover for G, with core-free intersection D = ⋂8 i=1Mi. Also for each i, 1 ≤ i ≤ 8 we assume that |G : Mi| = αi such that α1 ≤ α2 ≤ α3 ≤ α4 ≤ α5 ≤ α6 ≤ α7 ≤ α8. Let G be a Cn-group, we say that G is a core i2-group if (Mi)G ∩ (Mj)G = 1 for 3 ≤ i < j ≤ 8. Also let G be a Cn-group and core i2-group, then we say that N := (M1)G ∩ (M2)G central core of G. In this paper we show that if G be a semisimple C8-group and αl ≤ 4 then G is core i-2 group. Also we give some results for central core of G. Mathematics Subject Classification: 20F99

Research paper thumbnail of Tuples with Property of Cyclicity Criterions

Journal of Mathematical Extension, 2013

In this paper we give conditions under which a tuple of operators satisfying the hypercyclicity, ... more In this paper we give conditions under which a tuple of operators satisfying the hypercyclicity, supercyclicity and cyclicity criterions.

Research paper thumbnail of C8-Groups and Nilpotency Condition

International Journal of Algebra, 2010

A cover for a group is a collection of proper subgroups whose union is the whole group. A cover i... more A cover for a group is a collection of proper subgroups whose union is the whole group. A cover is irredundant if no proper sub-collection is also a cover and is called maximal if all its members are maximal subgroups. For an integer n > 2, a cover with n members is called an n-cover. In this paper we characterize all nilpotent groups have a maximal irredundant 8-cover with core-free intersection.

Research paper thumbnail of Covering Semisimple Groups by Subgroups

International Journal of Algebra, 2011

A cover for a group is a collection of proper subgroups whose union is the whole group. A cover i... more A cover for a group is a collection of proper subgroups whose union is the whole group. A cover is irredundant if no proper sub-collection is also a cover and is called maximal if all its members are maximal subgroups. For an integer n > 2, a cover with n members is called an n-cover. A cover C for a group G is called a C n-cover whenever C is an irredundant maximal core-free n-cover for G and in this case we say that G is a C n-group. Let G denote a semisimple C 8-group and {M i |1 ≤ i ≤ 8} be a maximal irredundant 8-cover for G, with core-free intersection D. Also for each i, 1 ≤ i ≤ 8 we assume that |G : M i | = α i such that α 1 ≤ α 2 ≤ α 3 ≤ α 4 ≤ α 5 ≤ α 6 ≤ α 7 ≤ α 8. In this paper we prove that If G is a C 8-group and α 1 ≤ α 2 ≤ 4 and α 3 = 6 then G is not semisimple.

Research paper thumbnail of The number of C8-groups for some primitive subgroups

International Journal of Algebra, 2014

In this paper we give the number of C 8-groups for some primitive subgroups.

Research paper thumbnail of Groups with a maximal irredundant 6-cover

A cover for a group G is a collection of proper subgroups whose union is the whole group G. A cov... more A cover for a group G is a collection of proper subgroups whose union is the whole group G. A cover is irredundant if no proper sub-collection is also a cover, and is called maximal if all its members are maximal subgroups. For an integer n &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt; 2, a cover with n members is called an n-cover. Also, we denote σ (G) = n

Research paper thumbnail of CHARACTERIZATION OF p-GROUPS WITH A MAXIMAL IRREDUNDANT 8COVER

A group is covered by a collection of subgroups if it is the union of the collection. The cover i... more A group is covered by a collection of subgroups if it is the union of the collection. The cover is irredundant if no proper sub-collection is also a cover. A cover in which all subgroups are maximal is called maximal. In this paper we completely characterize p-groups (p is a prime) with a maximal irredundant 8-cover with core-free intersection.

Research paper thumbnail of Minimal Blocking Sets in PG ( n , 2) and Covering Groups by Subgroups

Communications in Algebra, 2008

In this paper we prove that a set of points B of P G(n, 2) is a minimal blocking set if and only ... more In this paper we prove that a set of points B of P G(n, 2) is a minimal blocking set if and only if B = P G(d, 2) with d odd and B is a set of d + 2 points of P G(d, 2) no d + 1 of them in the same hyperplane. As a corollary to the latter result we show that if G is a finite 2-group and n is a positive integer, then G admits a C n+1 -cover if and only if n is even and G ∼ = (C 2 ) n , where by a Cm-cover for a group H we mean a set C of size m of maximal subgroups of H whose set-theoretic union is the whole H and no proper subset of C has the latter property and the intersection of the maximal subgroups is core-free. Also for all n < 10 we find all pairs (m, p) (m > 0 an integer and p a prime number) for which there is a blocking set B of size n in P G(m, p) such that B = P G(m, p).