On infinite groups with given properties of the norm of infinite subgroups

被引：0
|
作者：
Liman F.M. [1 ]
Lukashova T.D. [1 ]
机构：
[1] Sumy Pedagogic University, Sumy
来源：
Ukrainian Mathematical Journal | 2001年 / 53卷 / 5期
关键词：
Finite Group; Finite Index; Finite Extension; Infinite Group; Nonperiodic Case;
D O I：
10.1023/A:1012526216221
中图分类号：
学科分类号：
摘要：
We investigate the relationship between the norm NG (∞) of infinite subgroups of an infinite group G and the structure of this group. We prove that NG (∞) is Abelian in the nonperiodic case, and a locally finite group is a finite extension of a quasicyclic subgroup if NG(∞) is a non-Dedekind group. In both cases, we describe the structure of the group G under the condition that the subgroup NG(∞) has finite index in G. © 2001 Plenum Publishing Corporation.
引用
收藏
页码：719 / 725
页数：6
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