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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...
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