A NOTE ON GROUPS WITH FINITE CONJUGACY CLASSES OF SUBNORMAL SUBGROUPS

被引：0

作者：

de Giovanni, Francesco ^{[1
]}

Saccomanno, Federica ^{[1
]}

机构：

[1] Univ Naples Federico II, Dipartimento Matemat & Applicaz, Complesso Univ Monte S Angelo,Via Cintia, I-80126 Naples, Italy

来源：

MATHEMATICA SLOVACA | 2017年 / 67卷 / 02期

关键词：

locally graded group; subnormal subgroup; conjugacy class;

D O I：

10.1515/ms-2016-0274

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A group G is said to be a V-group if every subnormal subgroup of G has only finitely many conjugates. It is proved here that if G is a group admitting an ascending normal series whose factors have finite rank, and all proper subgroups of G have the V-property, then G itself is a V-group, provided that G belongs to a suitable class of generalized soluble groups, containing in particular all locally (soluble-by-finite) groups. On the other hand, an example shows that there exist periodic metabelian minimal non-V groups. (C) 2017 Mathematical Institute Slovak Academy of Sciences

引用

页码：387 / 390

页数：4

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