On locally finite groups with a four-subgroup whose centralizer is small

被引：1

作者：

Lima, Enio ^{[1
]}

Shumyatsky, Pavel ^{[1
]}

机构：

[1] Univ Brasilia, Dept Math, BR-70919 Brasilia, DF, Brazil

来源：

MONATSHEFTE FUR MATHEMATIK | 2013年 / 172卷 / 01期

关键词：

Locally finite groups; Centralizers; PERIODIC-GROUPS; PRIME-ORDER; SOLUBLE GROUPS; ELEMENT;

D O I：

10.1007/s00605-012-0462-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a locally finite group which contains a non-cyclic subgroup V of order four such that C-G (V) is finite and C-G (phi) has finite exponent for some phi is an element of V. We show that [ G, phi]' has finite exponent. This enables us to deduce that G has a normal series 1 <= G(1) <= G(2) <= G(3) <= G such that G(1) and G/G(2) have finite exponents while G(2)/G(1) is abelian. Moreover G(3) is hyperabelian and has finite index in G.

引用

页码：77 / 84

页数：8

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