scholarly journals Groups with boundedly finite conjugacy classes of commutators

2018 ◽  
Vol 69 (3) ◽  
pp. 1047-1051 ◽  
Author(s):  
Gláucia Dierings ◽  
Pavel Shumyatsky
Keyword(s):  
Conjugacy Classes ◽  
Finite Conjugacy

Groups with finite conjugacy classes of non-subnormal subgroups

1998 ◽  
Vol 70 (3) ◽  
pp. 169-181 ◽  
Author(s):  
S. Franciosi ◽  
F. de Giovanni ◽  
L.A. Kurdachenko
Keyword(s):  
Conjugacy Classes ◽  
Finite Conjugacy ◽  
Subnormal Subgroups

Groups with Finiteness Conditions on Commutators

2012 ◽  
Vol 19 (spec01) ◽  
pp. 1197-1204
Author(s):  
Maria De Falco ◽  
Francesco de Giovanni ◽  
Carmela Musella
Keyword(s):  
Conjugacy Classes ◽  
Finiteness Conditions ◽  
Finite Conjugacy

The structure of groups for which certain sets of commutator subgroups are finite is investigated. In particular, the relation between such groups and groups with finite conjugacy classes of elements is discussed.

Maximal subgroups of GL n (D) with finite conjugacy classes

2009 ◽  
Vol 130 (3) ◽  
pp. 287-293 ◽  
Author(s):  
Dariush Kiani ◽  
Mojtaba Ramezan-Nassab
Keyword(s):  
Conjugacy Classes ◽  
Maximal Subgroups ◽  
Finite Conjugacy

Weak Cayley tables and generalized centralizer rings of finite groups

2012 ◽  
Vol 153 (2) ◽  
pp. 281-318 ◽  
Author(s):  
STEPHEN P. HUMPHRIES ◽  
EMMA L. RODE
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Conjugacy Classes ◽  
Cayley Table ◽  
A Finite Group ◽  
Finite Conjugacy ◽  
Relationship Of ◽  
Cayley Tables ◽  
The Relationship

AbstractFor a finite group G we study certain rings (k)G called k-S-rings, one for each k ≥ 1, where (1)G is the centraliser ring Z(ℂG) of G. These rings have the property that (k+1)G determines (k)G for all k ≥ 1. We study the relationship of (2)G with the weak Cayley table of G. We show that (2)G and the weak Cayley table together determine the sizes of the derived factors of G (noting that a result of Mattarei shows that (1)G = Z(ℂG) does not). We also show that (4)G determines G for any group G with finite conjugacy classes, thus giving an answer to a question of Brauer. We give a criteria for two groups to have the same 2-S-ring and a result guaranteeing that two groups have the same weak Cayley table. Using these results we find a pair of groups of order 512 that have the same weak Cayley table, are a Brauer pair, and have the same 2-S-ring.

A NILPOTENCY-LIKE CONDITION FOR INFINITE GROUPS

2018 ◽  
Vol 105 (1) ◽  
pp. 24-33
Author(s):  
M. DE FALCO ◽  
F. DE GIOVANNI ◽  
C. MUSELLA ◽  
N. TRABELSI
Keyword(s):  
Normal Subgroup ◽  
Positive Integer ◽  
Finite Index ◽  
Conjugacy Classes ◽  
Nilpotent Subgroup ◽  
Infinite Groups ◽  
Finite Conjugacy

If $k$ is a positive integer, a group $G$ is said to have the $FE_{k}$-property if for each element $g$ of $G$ there exists a normal subgroup of finite index $X(g)$ such that the subgroup $\langle g,x\rangle$ is nilpotent of class at most $k$ for all $x\in X(g)$. Thus, $FE_{1}$-groups are precisely those groups with finite conjugacy classes ($FC$-groups) and the aim of this paper is to extend properties of $FC$-groups to the case of groups with the $FE_{k}$-property for $k>1$. The class of $FE_{k}$-groups contains the relevant subclass $FE_{k}^{\ast }$, consisting of all groups $G$ for which to every element $g$ there corresponds a normal subgroup of finite index $Y(g)$ such that $\langle g,U\rangle$ is nilpotent of class at most $k$, whenever $U$ is a nilpotent subgroup of class at most $k$ of $Y(g)$.

scholarly journals A reduction theorem for perfect locally finite minimal non-FC groups

1999 ◽  
Vol 41 (1) ◽  
pp. 81-83 ◽  
Author(s):  
FELIX LEINEN
Keyword(s):  
Conjugacy Class ◽  
Proper Subgroup ◽  
Conjugacy Classes ◽  
The Other ◽  
Reduction Theorem ◽  
Locally Finite ◽  
Open Question ◽  
Finite Conjugacy

A group G is said to be a minimal non-FC group, if G contains an infinite conjugacy class, while every proper subgroup of G merely has finite conjugacy classes. The structure of imperfect minimal non-FC groups is quite well-understood. These groups are in particular locally finite. At the other end of the spectrum, a perfect locally finite minimal non-FC group must be a p-group. And it has been an open question for quite a while now, whether such groups exist or not.

scholarly journals GROUPS WITH THE MAXIMAL CONDITION ON NON-BFC SUBGROUPS. II

2002 ◽  
Vol 45 (3) ◽  
pp. 513-522
Author(s):  
Martyn R. Dixon ◽  
Leonid A. Kurdachenko
Keyword(s):  
Finite Groups ◽  
Conjugacy Classes ◽  
Subject Classification ◽  
Finitely Generated ◽  
Maximal Condition ◽  
Primary 20E15 ◽  
Secondary 20F16 ◽  
Finite Conjugacy

AbstractA group $G$ is called a group with boundedly finite conjugacy classes (or a BFC-group) if $G$ is finite-by-abelian. A group $G$ satisfies the maximal condition on non-BFC-subgroups if every ascending chain of non-BFC-subgroups terminates in finitely many steps. In this paper the authors obtain the structure of finitely generated soluble-by-finite groups with the maximal condition on non-BFC subgroups.AMS 2000 Mathematics subject classification: Primary 20E15. Secondary 20F16; 20F24

scholarly journals Groups of infinite rank with finite conjugacy classes of subnormal subgroups

2015 ◽  
Vol 431 ◽  
pp. 24-37
Author(s):  
M. De Falco ◽  
F. de Giovanni ◽  
C. Musella ◽  
N. Trabelsi
Keyword(s):  
Conjugacy Classes ◽  
Infinite Rank ◽  
Finite Conjugacy ◽  
Subnormal Subgroups
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