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Algebra and Discrete Mathematics, 2009, Issue 4, Pages 158–166
(Mi adm149)
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This article is cited in 1 scientific paper (total in 1 paper)
RESEARCH ARTICLE
Groups with many generalized $FC$-subgroup
Alessio Russoa, Giovanni Vincenzib a Dipartimento di Matematica, SecondaUniversità di Napoli, Via Vivaldi 43, I – 81100 Caserta (Italy)
b Dipartimento di Matematica e Informatica, Universitá di Salerno, Via Ponte Don Melillo, I – 84084 Fisciano, Salerno (Italy)
Abstract:
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:
Conjugacy class, $FC$-groups, normalizer subgroup, subnormal subgroup.
Received: 11.07.2009 Revised: 11.07.2009
Citation:
Alessio Russo, Giovanni Vincenzi, “Groups with many generalized $FC$-subgroup”, Algebra Discrete Math., 2009, no. 4, 158–166
Linking options:
https://www.mathnet.ru/eng/adm149 https://www.mathnet.ru/eng/adm/y2009/i4/p158
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