Groups with Restricted Conjugacy Classes

de Giovanni, F., Russo, A., and Vincenzi, G.. "Groups with Restricted Conjugacy Classes." Serdica Mathematical Journal 28.3 (2002): 241-254. <http://eudml.org/doc/11560>.

@article{deGiovanni2002,
abstract = {Let F C 0 be the class of all finite groups, and for each nonnegative integer n define by induction the group class FC^(n+1) consisting of all groups G such that for every element x the factor group G/CG ( <x>^G ) has the property FC^n . Thus FC^1 -groups are precisely groups with finite conjugacy classes, and the class FC^n obviously contains all finite groups and all nilpotent groups with class at most n. In this paper the known theory of FC-groups is taken as a model, and it is shown that many properties of FC-groups have an analogue in the class of FC^n -groups.},
author = {de Giovanni, F., Russo, A., Vincenzi, G.},
journal = {Serdica Mathematical Journal},
keywords = {Conjugacy Class; Nilpotent Group; conjugacy classes; nilpotent groups; FC-groups; derived series; elements of finite order; chief factors; maximal subgroups; subgroups of finite index; transitive normality},
language = {eng},
number = {3},
pages = {241-254},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Groups with Restricted Conjugacy Classes},
url = {http://eudml.org/doc/11560},
volume = {28},
year = {2002},
}

TY - JOUR
AU - de Giovanni, F.
AU - Russo, A.
AU - Vincenzi, G.
TI - Groups with Restricted Conjugacy Classes
JO - Serdica Mathematical Journal
PY - 2002
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 28
IS - 3
SP - 241
EP - 254
AB - Let F C 0 be the class of all finite groups, and for each nonnegative integer n define by induction the group class FC^(n+1) consisting of all groups G such that for every element x the factor group G/CG ( <x>^G ) has the property FC^n . Thus FC^1 -groups are precisely groups with finite conjugacy classes, and the class FC^n obviously contains all finite groups and all nilpotent groups with class at most n. In this paper the known theory of FC-groups is taken as a model, and it is shown that many properties of FC-groups have an analogue in the class of FC^n -groups.
LA - eng
KW - Conjugacy Class; Nilpotent Group; conjugacy classes; nilpotent groups; FC-groups; derived series; elements of finite order; chief factors; maximal subgroups; subgroups of finite index; transitive normality
UR - http://eudml.org/doc/11560
ER -