Improving Thompson's Conjecture for Suzuki Groups

被引：2

作者：

Akhlaghi, Zeinab ^{[1
]}

Khatami, Maryam ^{[2
]}

机构：

[1] Amirkabir Univ Technol, Tehran Polytech, Fac Math & Comp Sci, Tehran 15914, Iran

[2] Univ Isfahan, Dept Math, Esfahan, Iran

来源：

COMMUNICATIONS IN ALGEBRA | 2016年 / 44卷 / 09期

关键词：

Conjugacy classes; Suzuki groups; Thompson's conjecture; CONJUGACY CLASS SIZES;

D O I：

10.1080/00927872.2015.1065871

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a finite group and cs(G) be the set of conjugacy class sizes of G. In 1987, J. G. Thompson conjectured that, if G is a finite group with Z(G)=1 and M is a nonabelian simple group satisfying that cs(G)=cs(M), then GM. This conjecture has been proved for Suzuki groups in [5]. In this article, we improve this result by proving that, if G is a finite group such that cs(G)=cs(Sz(q)), for q=2(2m+1), then GSz(q)xA, where A is abelian. We avoid using classification of finite simple groups in our proofs.

引用

页码：3927 / 3932

页数：6

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