Geodesic
Groups with many generalized $FC$-subgroup
Algebra and discrete mathematics, no. 4 (2009), pp. 158-166.

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Let $FC^0$ be the class of all finite groups, and for each non-negative integer $m$ define by induction the group class $FC^{m+1}$ consisting of all groups $G$ such that the factor group $G/C_G(x^G)$ has the property $FC^m$ for all elements $x$ of $G$. Clearly, $FC^1$ is the class of $FC$-groups and every nilpotent group with class at most $m$ belongs to $FC^m$. The class of $FC^m$-groups was introduced in [6]. In this article the structure of groups with finitely many normalizers of non-$FC^m$-subgroups (respectively, the structure of groups whose subgroups either are subnormal with bounded defect or have the property $FC^m$) is investigated.
Keywords: $FC$-groups, normalizer subgroup, subnormal subgroup.
Mots-clés : Conjugacy class 
@article{ADM_2009_4_a11,
     author = {Alessio Russo and Giovanni Vincenzi},
     title = {Groups with many generalized $FC$-subgroup},
     journal = {Algebra and discrete mathematics},
     pages = {158--166},
     publisher = {mathdoc},
     number = {4},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2009_4_a11/}
}
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Alessio Russo; Giovanni Vincenzi. Groups with many generalized $FC$-subgroup. Algebra and discrete mathematics, no. 4 (2009), pp. 158-166. http://geodesic.mathdoc.fr/item/ADM_2009_4_a11/