Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Mathematical Journal, Vol. 28, No 3, (2002), 241p-254p
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.
