Alessio Russo | Università della Campania Luigi Vanvitelli (original) (raw)
Papers by Alessio Russo
Central European Journal of Mathematics, Feb 1, 2011
This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We char... more This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We characterize the structure of such G in case they are locally finite. If G is a hyperabelian group and has the property, we show that every subgroup of G is in fact ascendant provided G is locally nilpotent or non-periodic. We also restrict our study replacing ascendant subgroups by permutable subgroups, which of course are ascendant [Stonehewer S.E., Permutable subgroups of infinite groups, Math
Mathematical Proceedings of the Royal Irish Academy, 2004
The class X of all groups whose non-normal subgroups have finite conjugacy classes has been inves... more The class X of all groups whose non-normal subgroups have finite conjugacy classes has been investigated. In particular, it will be proved that a soluble-by-finite X-group is locally (central-byfinite) and its commutator subgroup is an F C-group. The structure of periodic X-groups with Chernikov commutator subgroup is described. *
Journal of Algebra and Its Applications, 2014
Let 0 be the class of all finite groups, and for each non-negative integer define by induction th... more Let 0 be the class of all finite groups, and for each non-negative integer define by induction the group class +1 consisting of all groups such that the factor group / ( ) has the property for all elements of . Clearly, 1 is the class of -groups and every nilpotent group with class at most belongs to . The class of -groups was introduced in . In this article the structure of groups with finitely many normalizers of non--subgroups (respectively, the structure of groups whose subgroups either are subnormal with bounded defect or have the property ) is investigated.
Bollettino dell Unione Matematica Italiana
In this paper groups are considered inducing groups of power automorphisms on each factor of thei... more In this paper groups are considered inducing groups of power automorphisms on each factor of their derived series. In particular, it is proved that soluble groups with such property have derived length at most 3, and that this bound is best possible.
Rendiconti del Seminario matematico della Università di Padova
Ricerche di Matematica
ABSTRACT
Ricerche di Matematica
In this article we investigate the structure of soluble groups G such that [H, K] = H ∩ K for all... more In this article we investigate the structure of soluble groups G such that [H, K] = H ∩ K for all proper distinct normal subgroups H and K of G. Moreover, also the class consisting of all soluble groups G such that [H, K] = {1} for all proper distinct normal subgroups H and K of G is considered.
Rendiconti del Seminario matematico della Università di Padova
© Rendiconti del Seminario Matematico della Università di Padova, 1999, tous droits réservés. L&a... more © Rendiconti del Seminario Matematico della Università di Padova, 1999, tous droits réservés. L'accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » (http://rendiconti.math.unipd.it/) implique l'ac-cord avec les conditions ...
Journal of Algebra and Its Applications
International Journal of Group Theory
Let G be a normal subgroup of the full automorphism group Aut(G) of a group G, and assume that In... more Let G be a normal subgroup of the full automorphism group Aut(G) of a group G, and assume that Inn(G) £ G. An endomorphism s of G is said to be G-central if s induces the the identity on the factor group G/CG(G). Clearly, if G = Inn(G), then a G-central endomorphism is a central endomorphism. In this article the conditions under which a G-central endomorphism of a group is an automorphism are investigated.
Bollettino dell Unione Matematica Italiana
In [T. W. Müller, An arithmetic theorem related to groups of bounded nilpotency class, J. Algebra... more In [T. W. Müller, An arithmetic theorem related to groups of bounded nilpotency class, J. Algebra 300 (2006), 10-15] T. W. Müller characterizes the positive integers n satisfying the property that every group of order n is nilpotent of class bounded by a fixed positive integer c. In this article a different proof of the above result will be given.
We continue the study of finite groups G such that, if H is a non-normal subgroup of G, then all ... more We continue the study of finite groups G such that, if H is a non-normal subgroup of G, then all normal subgroups of H are normal in the normalizer of H in G.
Ricerche di Matematica
We study the finite groups G such that, if H is a non-normal subgroup of G, then all normal subgr... more We study the finite groups G such that, if H is a non-normal subgroup of G, then all normal subgroups of H are normal in the normalizer of H in G.
Rendiconti del Circolo Matematico di Palermo, 2001
Central European Journal of Mathematics, Feb 1, 2011
This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We char... more This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We characterize the structure of such G in case they are locally finite. If G is a hyperabelian group and has the property, we show that every subgroup of G is in fact ascendant provided G is locally nilpotent or non-periodic. We also restrict our study replacing ascendant subgroups by permutable subgroups, which of course are ascendant [Stonehewer S.E., Permutable subgroups of infinite groups, Math
Mathematical Proceedings of the Royal Irish Academy, 2004
The class X of all groups whose non-normal subgroups have finite conjugacy classes has been inves... more The class X of all groups whose non-normal subgroups have finite conjugacy classes has been investigated. In particular, it will be proved that a soluble-by-finite X-group is locally (central-byfinite) and its commutator subgroup is an F C-group. The structure of periodic X-groups with Chernikov commutator subgroup is described. *
Journal of Algebra and Its Applications, 2014
Let 0 be the class of all finite groups, and for each non-negative integer define by induction th... more Let 0 be the class of all finite groups, and for each non-negative integer define by induction the group class +1 consisting of all groups such that the factor group / ( ) has the property for all elements of . Clearly, 1 is the class of -groups and every nilpotent group with class at most belongs to . The class of -groups was introduced in . In this article the structure of groups with finitely many normalizers of non--subgroups (respectively, the structure of groups whose subgroups either are subnormal with bounded defect or have the property ) is investigated.
Bollettino dell Unione Matematica Italiana
In this paper groups are considered inducing groups of power automorphisms on each factor of thei... more In this paper groups are considered inducing groups of power automorphisms on each factor of their derived series. In particular, it is proved that soluble groups with such property have derived length at most 3, and that this bound is best possible.
Rendiconti del Seminario matematico della Università di Padova
Ricerche di Matematica
ABSTRACT
Ricerche di Matematica
In this article we investigate the structure of soluble groups G such that [H, K] = H ∩ K for all... more In this article we investigate the structure of soluble groups G such that [H, K] = H ∩ K for all proper distinct normal subgroups H and K of G. Moreover, also the class consisting of all soluble groups G such that [H, K] = {1} for all proper distinct normal subgroups H and K of G is considered.
Rendiconti del Seminario matematico della Università di Padova
© Rendiconti del Seminario Matematico della Università di Padova, 1999, tous droits réservés. L&a... more © Rendiconti del Seminario Matematico della Università di Padova, 1999, tous droits réservés. L'accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » (http://rendiconti.math.unipd.it/) implique l'ac-cord avec les conditions ...
Journal of Algebra and Its Applications
International Journal of Group Theory
Let G be a normal subgroup of the full automorphism group Aut(G) of a group G, and assume that In... more Let G be a normal subgroup of the full automorphism group Aut(G) of a group G, and assume that Inn(G) £ G. An endomorphism s of G is said to be G-central if s induces the the identity on the factor group G/CG(G). Clearly, if G = Inn(G), then a G-central endomorphism is a central endomorphism. In this article the conditions under which a G-central endomorphism of a group is an automorphism are investigated.
Bollettino dell Unione Matematica Italiana
In [T. W. Müller, An arithmetic theorem related to groups of bounded nilpotency class, J. Algebra... more In [T. W. Müller, An arithmetic theorem related to groups of bounded nilpotency class, J. Algebra 300 (2006), 10-15] T. W. Müller characterizes the positive integers n satisfying the property that every group of order n is nilpotent of class bounded by a fixed positive integer c. In this article a different proof of the above result will be given.
We continue the study of finite groups G such that, if H is a non-normal subgroup of G, then all ... more We continue the study of finite groups G such that, if H is a non-normal subgroup of G, then all normal subgroups of H are normal in the normalizer of H in G.
Ricerche di Matematica
We study the finite groups G such that, if H is a non-normal subgroup of G, then all normal subgr... more We study the finite groups G such that, if H is a non-normal subgroup of G, then all normal subgroups of H are normal in the normalizer of H in G.
Rendiconti del Circolo Matematico di Palermo, 2001