INFINITE GROUPS WITH TWO CONJUGACY CLASSES OF NON-SUBNORMAL SUBGROUPS

2016 ◽  
Vol 38 (5) ◽  
pp. 489-497
Author(s):  
Aifang Feng ◽  
Zuhua Liu
Keyword(s):  
Conjugacy Classes ◽  
Infinite Groups ◽  
Subnormal Subgroups

Infinite groups with a generalized dense system of subnormal subgroups

1982 ◽  
Vol 33 (3) ◽  
pp. 313-316
Author(s):  
L. A. Kurdachenko ◽  
N. F. Kuzennyi ◽  
V. V. Pylaev
Keyword(s):  
Infinite Groups ◽  
Dense System ◽  
Subnormal Subgroups

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

Some generalizations of normal series in infinite groups

1972 ◽  
Vol 14 (4) ◽  
pp. 496-502 ◽  
Author(s):  
Richard E. Phillips
Keyword(s):  
Finite Length ◽  
Infinite Groups ◽  
Normal Series ◽  
Group A ◽  
Complete Series ◽  
Image Position ◽  
Subnormal Subgroups

In this paper, we are concerned with certain generalizations of subnormal and ascendent (transfinitely subnormal) subgroups of a group. A subgroup A of a group G is called f-ascendent in G if there is a well ordered ascending complete series of subgroups of G, where for all α < λ, either Gα ⊲ Gα+1 or [Gα+1: Gα] < ∞. If such a series has finite length, A is called F-subnormal in G.

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 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

Maximal Subgroups of Subnormal Subgroups ofGLn(D) with Finite Conjugacy Classes

2010 ◽  
Vol 39 (1) ◽  
pp. 169-175 ◽  
Author(s):  
Dariush Kiani ◽  
Mojtaba Ramezan-Nassab
Keyword(s):  
Conjugacy Classes ◽  
Maximal Subgroups ◽  
Finite Conjugacy ◽  
Subnormal Subgroups

A note on groups with finite conjugacy classes of subnormal subgroups

2017 ◽  
Vol 67 (2) ◽  
Author(s):  
Francesco de Giovanni ◽  
Federica Saccomanno
Keyword(s):  
Conjugacy Classes ◽  
Finite Conjugacy ◽  
Subnormal Subgroups

AbstractA group

Subnormal structure in some classes of infinite groups

1973 ◽  
Vol 8 (1) ◽  
pp. 137-150 ◽  
Author(s):  
D.J. McCaughan
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Intersection Property ◽  
Infinite Groups ◽  
Subnormal Structure ◽  
Torsion Free ◽  
Subnormal Subgroups

Let p be a prime and G a group with a p–reduced nilpotent normal subgroup N such that G/N is a nilpotent p–group. It is shown that if G has the subnormal intersection property and if G/N is finite or N is p–torsion-free, then G is nilpotent. This result is used to prove that an abelian-by-finite group has the subnormal intersection property if and only if it has a bound for the subnormal indices of its subnormal subgroups.

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
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