Finite Groups with Seminormal Sylow Subgroups

被引：12

作者：

Guo, Wen Bin ^{[1
,2
]}

机构：

[1] Xuzhou Normal Univ, Dept Math, Xuzhou 221116, Peoples R China

[2] Univ Sci & Technol China, Dept Math, Hefei 230026, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2008年 / 24卷 / 10期

关键词：

finite groups; seminormal subgroups; Sylow subgroups; p-soluble groups; p-supersoluble groups;

D O I：

10.1007/s10114-008-6563-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove the following theorem: Let p be a prime number, P a Sylow p-subgroup of a group G and pi = pi(G) \ {p}. If P is seminormal in G, then the following statements hold: 1) G is a p-soluble group and P' <= O-p(G); 2) l(p)(G) <= 2 and l(pi)(G) <= 2; 3) if a pi-Hall subgroup of G is q-supersoluble for some q is an element of pi, then G is q-supersoluble.

引用

页码：1751 / 1757

页数：7

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