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

被引：20

作者：

Gordeev, Nikolai ^{[2
]}

Grunewald, Fritz ^{[3
]}

Kunyavskii, Boris ^{[1
]}

Plotkin, Eugene ^{[1
]}

机构：

[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

来源：

JOURNAL OF ALGEBRA | 2010年 / 323卷 / 10期

关键词：

Finite group; Solvable radical; Simple algebraic group; Finite field; FINITE SOLUBLE GROUPS; MAXIMAL-SUBGROUPS; CONJUGACY CLASSES; ELEMENTS; NUMBER; LAWS;

D O I：

10.1016/j.jalgebra.2010.01.032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：2888 / 2904

页数：17

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