On the sharp Baer-Suzuki theorem for the π-radical of a finite group

被引:7
作者
Yang, N. [1 ]
Wu, Zh. [1 ]
Revin, D. O. [2 ,3 ]
Vdovin, E. P. [2 ,3 ]
机构
[1] Jiangnan Univ, Wuxi, Jiangsu, Peoples R China
[2] Russian Acad Sci, Siberian Branch, Sobolev Inst Math, Novosibirsk, Russia
[3] Novosibirsk State Univ, Novosibirsk, Russia
基金
俄罗斯基础研究基金会;
关键词
simple linear groups; simple unitary groups; pi-radical of a group; Baer-Suzuki pi-theorem; CLASSIFICATION; SUBGROUPS; CRITERIA;
D O I
10.4213/sm9698e
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let pi be a proper subset of the set of prime numbers. Denote by r the least prime not contained in pi and set m = r for r = 2 and 3 and m = r - 1 for r >= 5. The conjecture under consideration claims that a conjugacy class D of a finite group G generates a pi-subgroup of G (equivalently, is contained in the pi-radical) if and only if any m elements of D generate a pi-group. It is shown that this conjecture holds if every non-Abelian composition factor of G is isomorphic to a sporadic, an alternating, a linear, or a unitary simple group.
引用
收藏
页码:108 / 147
页数:40
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