Variations on the Baer-Suzuki theorem

被引：10

作者：

Guralnick, Robert ^{[1
]}

Malle, Gunter ^{[2
]}

机构：

[1] Univ So Calif, Dept Math, Los Angeles, CA 90089 USA

[2] TU Kaiserslautern, FB Math, D-67653 Kaiserslautern, Germany

来源：

MATHEMATISCHE ZEITSCHRIFT | 2015年 / 279卷 / 3-4期

基金：

美国国家科学基金会;

关键词：

Baer-Suzuki theorem; Conjugacy classes; Commutators; CONJUGACY CLASSES; CHARACTER TABLES; FINITE-GROUPS; SUBGROUPS;

D O I：

10.1007/s00209-014-1399-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Baer-Suzuki theorem says that if is a prime, is a -element in a finite group and is a -group for all , then the normal closure of in is a -group. We consider the case where is replaced by for some other -element . While the analog of Baer-Suzuki is not true, we show that some variation is. We also answer a closely related question of Pavel Shumyatsky on commutators of conjugacy classes of -elements.

引用

页码：981 / 1006

页数：26

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