Finite groups whose maximal subgroups of sylow p-subgroups admit a p-solvable supplement

被引：7
|
作者：
Qian GuoHua [1 ]
机构：
[1] Changshu Inst Technol, Dept Math, Changshu 215500, Peoples R China
来源：
SCIENCE CHINA-MATHEMATICS | 2013年 / 56卷 / 05期
基金：
中国国家自然科学基金;
关键词：
finite group; p-solvable group; Sylow subgroup; supplement;
D O I：
10.1007/s11425-012-4485-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this note, we show that if every maximal subgroup of a Sylow p-subgroup of a finite group has a p-solvable supplement then the group is necessarily p-solvable. This gives a positive answer to Problem 17.111 of the Kourovka Notebook (Unsolved Problems in Group Theory), which was posed by Skiba.
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页码：1015 / 1018
页数：4
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