Short two-variable identities for finite groups

被引：2

作者：

Cargo, David P. ^{[1
]}

de Launey, Warwick ^{[2
]}

Liebeck, Martin W. ^{[3
]}

Stafford, Richard M. ^{[1
]}

机构：

[1] US Dept Def, Ft George G Meade, MD 20755 USA

[2] Ctr Commun Res, La Jolla, CA 92121 USA

[3] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

来源：

JOURNAL OF GROUP THEORY | 2008年 / 11卷 / 05期

关键词：

D O I：

10.1515/JGT.2008.043

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider finite groups G satisfying identities of the form x(e1)y(f1)x(e2)y(f2) ... x(er)y(fr) =1. We focus on identities with r small, Sigma(i) e(i) = Sigma(i) f(i) = 0, and all e(i), f(i) coprime to the order of G. We show that for r = 2, 3 and 5, G must be nilpotent. We also classify for r = 4, 6 and 7, the special identities which can hold in non-nilpotent groups. Finally, we show that for r < 30. the group G must be solvable.

引用

页码：675 / 690

页数：16

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