Commutators of elements of coprime orders in finite groups

被引：13
|
作者：
Shumyatsky, Pavel [1 ]
机构：
[1] Univ Brasilia, Dept Math, BR-70910900 Brasilia, DF, Brazil
来源：
FORUM MATHEMATICUM | 2015年 / 27卷 / 01期
关键词：
Finite groups; commutators; alternating groups;
D O I：
10.1515/forum-2012-0127
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is an attempt to find out which properties of a finite group G can be expressed in terms of commutators of elements of coprime orders. A criterion of solubility of G in terms of such commutators is obtained. We also conjecture that every element of a nonabelian simple group is a commutator of elements of coprime orders and we confirm this conjecture for the alternating groups.
引用
收藏
页码：575 / 583
页数：9
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