ON SOLUBILITY OF GROUPS WITH BOUNDED CENTRALIZER CHAINS

被引：11
|
作者：
Khukhro, E. I. [1 ]
机构：
[1] Sobolev Inst Math, Novosibirsk 630090, Russia
来源：
GLASGOW MATHEMATICAL JOURNAL | 2009年 / 51卷
关键词：
MINIMAL-CONDITION; PSEUDOFINITE GROUPS; SOLUBLE GROUPS; NILPOTENCY;
D O I：
10.1017/S0017089508004527
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The c-dimension of it group is the maximum length of a chain of nested centralizers. It is proved that a periodic locally soluble group of finite c-dimension k is soluble of derived length bounded in terms of k, and the rank of its quotient by the Hirsch-Plotkin radical is bounded in terms of k. Corollary: a pseudo-(finite Soluble) group of finite c-dimension k is soluble of derived length bounded in terms of k.
引用
收藏
页码：49 / 54
页数：6
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