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可解群的若干充分条件
引用本文:王丽芳,张勤海.可解群的若干充分条件[J].数学季刊,2006,21(3):351-357.
作者姓名:王丽芳  张勤海
作者单位:Department of Computer and Mathematics,Shanxi Teacher's University,Linfen 041004,China
基金项目:Supported by the NSF of China(10471085) Supported by the Shanxi Province(20051007) Supported by the Returned Chinese Students Found of Shanxi Province(Jinliuguanban [2004]7)
摘    要:A subgroup if of a group G is called semipermutable if it is permutable with every subgroup K of G with (|H|, |K|) - 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with (p, |H|) = 1. In this paper, some sufficient conditions for a group to be solvable are obtained in terms of s-semipermutability.

关 键 词:可解群  半交换次群  群论  充分条件

Some Sufficient Conditions of a Solvable Group
WANG Li-fang,ZHANG Qin-hai.Some Sufficient Conditions of a Solvable Group[J].Chinese Quarterly Journal of Mathematics,2006,21(3):351-357.
Authors:WANG Li-fang  ZHANG Qin-hai
Abstract:A subgroup if of a group G is called semipermutable if it is permutable with every subgroup K of G with (|H|, |K|) - 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with (p, |H|) = 1. In this paper, some sufficient conditions for a group to be solvable are obtained in terms of s-semipermutability.
Keywords:a solvable group  a s-semipermutable subgroup  a semipermutable subgroup
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