# Groups with Restricted Conjugacy Classes

de Giovanni, F.; Russo, A.; Vincenzi, G.

Serdica Mathematical Journal (2002)

- Volume: 28, Issue: 3, page 241-254
- ISSN: 1310-6600

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topde 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 -

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