From Thompson to Baer-Suzuki: A sharp characterization of the solvable radical

JOURNAL OF ALGEBRA

卷:323

Article

Gordeev, Nikolai²  Grunewald, Fritz³  Kunyavskii, Boris¹  Plotkin, Eugene¹ 

[1] Bar Ilan Univ, Dept Math, IL-52900 Ramat Gan, Israel

[2] Herzen State Pedag Univ, Dept Math, St Petersburg 191186, Russia

[3] Univ Dusseldorf, Math Inst, D-40225 Dusseldorf, Germany

关键词: Finite group;    Solvable radical;    Simple algebraic group;    Finite field;   

DOI  :  10.1016/j.jalgebra.2010.01.032

来源: Elsevier

【 摘 要 】

We prove that an element g of prime order > 3 belongs to the solvable radical R(G) of a finite (or, more generally, a linear) group if and only if for every x is an element of G the subgroup generated by g, xgx(-1) is solvable. This theorem implies that a finite (or a linear) group G is solvable if and only if in each conjugacy class of G every two elements generate a solvable subgroup. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free