Further solvable analogues of the Baer-Suzuki theorem and generation of nonsolvable groups

JOURNAL OF ALGEBRA

卷:360

Article

Guest, Simon¹ 

[1] Baylor Univ, Dept Math, Waco, TX 76798 USA

关键词: Solvable radical;    Generation by conjugates;   

DOI  :  10.1016/j.jalgebra.2012.03.014

来源: Elsevier

【 摘 要 】

Let G be an almost simple group. We prove that if x is an element of G has prime order p >= 5, then there exists an involution y such that < x, y > is not solvable. Also, if x is an involution then there exist three conjugates of x that generate a nonsolvable group, unless x belongs to a short list of exceptions, which are described explicitly. We also prove that if x has order 6 or 9, then there exist two conjugates that generate a nonsolvable group. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free