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.
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页码：1751 / 1757
页数：7
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