Alessio Russo

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Oludamini Ogunnaike

University of Virginia

Mathieu Marion

Université du Québec à Montréal

Jan N . Bremmer

University of Groningen

Bálint Forgács

Eötvös Loránd University Budapest

Bárbara Sampedro

Universidad de Buenos Aires

Ana Isabel Jiménez San Cristóbal

Universidad Complutense de Madrid

Gabriel C Avila

Universidade Federal do Recôncavo da Bahia

Gerardo Ienna

Sapienza, Università di Roma

Adolfo Vasquez Rocca

Universidad Complutense de Madrid

Marcelo Carvalho

Universidade Federal de São Paulo (UNIFESP)

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Papers by Alessio Russo

On groups with a restriction on normal subgroups

International Journal of Group Theory, Mar 1, 2018

The structure of infinite groups in which every (proper) normal subgroup is the only one of its c... more

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Some theorems of Fitting type *

Advances in Group Theory and Applications, 2019

Let W be the class consisting of all groups G such that, if N is a normal subgroup of the term G ... more Let W be the class consisting of all groups G such that, if N is a normal subgroup of the term G (α) of the derived series of G, for some ordinal α, then N is normal in G. Clearly, W contains the class T of groups in which normality is a transitive relation studied by many authors. In this article we will prove, among other results, that a group which is the product of finitely many normal (generalized) soluble W-subgroups is locally supersoluble.

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Groups with many generalized-subgroup

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 [6]. 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.

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A note on fixed points of automorphisms of infinite groups

International Journal of Group Theory, 2014

‎Motivated by a celebrated theorem of Schur‎, ‎we show that if $Gamma$ is a normal subgroup of th... more ‎Motivated by a celebrated theorem of Schur‎, ‎we show that if $Gamma$ is a normal subgroup of the full automorphism group $Aut(G)$ of a group $G$ such that $Inn(G)$ is contained in $Gamma$ and $Aut(G)/Gamma$ has no uncountable abelian subgroups of prime exponent‎, ‎then $[G,Gamma]$ is finite‎, ‎provided that the subgroup consisting of all elements of $G$ fixed by $Gamma$ has finite index‎. ‎Some applications of this result are also given.‎

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On central endomorphisms of a group

International Journal of Group Theory, 2015

Let be a normal subgroup of the full automorphism group Aut(G) of a group G, and assume that Inn(... more Let be a normal subgroup of the full automorphism group Aut(G) of a group G, and assume that Inn(G) . An endomorphism of G is said to be -central if induces the the identity on the factor group G=CG(). Clearly, if = Inn(G), then a -central endomorphism is a central endomorphism. In this article the conditions under which a -central endomorphism of a group is an automorphism are investigated.

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Groups satisfying the minimal condition on subgroups which are not transitively normal

Rendiconti del Circolo Matematico di Palermo Series 2, 2021

A subgroupXof a groupGis calledtransitively normalifXis normal in any subgroup YofGsuch that$$X\l... more A subgroupXof a groupGis calledtransitively normalifXis normal in any subgroup YofGsuch that$$X\le Y$$X≤YandXis subnormal inY. Thus all subgroups of a groupGare transitively normal if and only if normality is a transitive relation in every subgroup ofG(i.e.Gis a$$\overline{T}$$T¯-group). It is proved that a groupGwith no infinite simple sections satisfies the minimal condition on subgroups that are not transitively normal if and only if either Gis Černikov or a$${\overline{T}}$$T¯-group.

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On Groups Satisfying the Maximal and the Minimal Conditions for Subnormal Subgroups of Infinite Order or Index

Bulletin of the Korean Mathematical Society, 2010

In this article we will prove that a generalized radical group satisfying the maximal condition f... more

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Groups in which every subgroup is almost pronormal

Note di Matematica, 2008

A subgroup of a group is called almost normal if it has only finitely many conjugates, or equival... more A subgroup of a group is called almost normal if it has only finitely many conjugates, or equivalently if its normalizer has finite index in the group. A famous theorem by B.H. Neumann states that all subgroups of a group G are almost normal if and only if the centre Z(G) has finite index in G. Here the structure of groups in which every subgroup is pronormal in a subgroup of finite index is investigated.

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Groups with Restricted Conjugacy Classes

Let F C0 be the class of all finite groups, and for each non- negative integer n define by induct... more Let F C0 be the class of all finite groups, and for each non- negative integer n define by induction the group class F Cn+1 consisting of all groups G such that for every element x the factor group G/CG(h xi G) has the property F Cn. Thus F C1-groups are precisely groups with finite conjugacy classes, and the class F Cn obviously contains all finite groups and all nilpotent groups with class at most n. In this paper the known theory of F C-groups is taken as a model, and it is shown that many properties of F C-groups have an analogue in the class of F Cn-groups.

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On groups whose subgroups are closed in the profinite topology

Journal of Pure and Applied Algebra, 2009

A group is called extended residually finite (ERF) if every subgroup is closed in the profinite t... more A group is called extended residually finite (ERF) if every subgroup is closed in the profinite topology. The ERF-property is studied for nilpotent groups, soluble groups, locally finite groups and FC-groups. A complete characterization is given of FC-groups which are ERF. 2000 Mathematics Subject Classification: Primary 20E26.

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Abnormal subgroups and Carter subgroups in some classes of infinite groups

Journal of Algebra, 2006

We study the relationship between Carter subgroups and groups satisfying the minimal condition on... more

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On Groups Which Contain No HNN-Extensions

International Journal of Algebra and Computation, 2007

A group is called HNN-free if it has no subgroups that are nontrivial HNN-extensions. We prove th... more A group is called HNN-free if it has no subgroups that are nontrivial HNN-extensions. We prove that finitely generated HNN-free implies virtually polycyclic for a large class of groups. We also consider finitely generated groups with no free subsemigroups of rank 2 and show that in many situations such groups are virtually nilpotent. Finally, as an application of our results, we determine the structure of locally graded groups in which every subgroup is pronormal, thus generalizing a theorem of Kuzennyi and Subbotin.

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Sui divisori di un numero intero

In this article a primality criterion due to Dirichlet (1838) will be investigated. The result is... more In this article a primality criterion due to Dirichlet (1838) will be investigated. The result is related to the so-called divisor function which counts the number of divisors of an integer. The criterion is also illustrated by an arrow which can be useful as a didactic tool to teach elementary topics in arithmetic.

Groups whose Non-Normal Subgroups have Finite Conjugacy Classes

Mathematical Proceedings of the Royal Irish Academy, 2004

We consider the class of all groups whose non-normal subgroups are FC-groups. In particular, it w... more We consider the class of all groups whose non-normal subgroups are FC-groups. In particular, it will be proved that if such a group is soluble-by-finite, then it is a locally FC-group and its commutator subgroup is an FC-group. We consider also the case when such groups have Chernikov commutator subgroups.

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On a class of subnormal endomorphisms of groups

Journal of Algebra and Its Applications

On numbers which are orders of nilpotent groups only

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.

Groups whose non-normal subgroups have a transitive normality relation

Rendiconti del Circolo Matematico di Palermo, 2001

This article investigates the structure of groups in which every subgroup either is subnormal or ... more

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Groups Whose Proper Subgroups Are Generalized FC-Groups

Journal of Algebra and Its Applications, 2011

Let 𝔛 be a class of groups. A group G is said to be minimal non-𝔛 if all proper subgroups of G ar... more Let 𝔛 be a class of groups. A group G is said to be minimal non-𝔛 if all proper subgroups of G are 𝔛-groups but G itself is not. The aim of this paper is to study the class of minimal non-FCn-groups, where FCn(n is a positive integer) is a class of generalized FC-groups introduced in [F. de Giovanni, A. Russo and G. Vincenzi, Groups with restricted conjugacy classes, Serdica Math. J.28 (2002) 241–254].

The Maximal and Minimal Conditions for Normal Subgroups of Infinite Order or Index

Communications in Algebra, 2005

ABSTRACT We study the structure of groups that satisfy the maximal conditions on infinite normal ... more ABSTRACT We study the structure of groups that satisfy the maximal conditions on infinite normal subgroups and the minimal condition on normal subgroups of infinite index. Characterizations of both properties are given in the general case. In addition, detailed information is obtained about the structure of soluble groups that satisfy these chain conditions.

Groups whose all subgroups are ascendant or self-normalizing

Central European Journal of Mathematics, 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. Z., 1972, 125(1), 1-16].

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On groups with a restriction on normal subgroups

International Journal of Group Theory, Mar 1, 2018

The structure of infinite groups in which every (proper) normal subgroup is the only one of its c... more

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Some theorems of Fitting type *

Advances in Group Theory and Applications, 2019

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Groups with many generalized-subgroup

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A note on fixed points of automorphisms of infinite groups

International Journal of Group Theory, 2014