Geodesic
Groups with Restricted Conjugacy Classes
Serdica Mathematical Journal, Tome 28 (2002) no. 3, pp. 241-254.

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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 ( ^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.
Keywords: Conjugacy Class, Nilpotent Group 
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     title = {Groups with {Restricted} {Conjugacy} {Classes}},
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de Giovanni, F.; Russo, A.; Vincenzi, G. Groups with Restricted Conjugacy Classes. Serdica Mathematical Journal, Tome 28 (2002) no. 3, pp. 241-254. http://geodesic.mathdoc.fr/item/SMJ2_2002_28_3_a5/