On <IMG BORDER="0" SRC="/proc/2004-132-08/S0002-9939-04-07296-X/gif-title0/img1.gif" >-supplemented maximal and minimal subgroups of Sylow subgroups of finite groups期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On -supplemented maximal and minimal subgroups of Sylow subgroups of finite groups

Authors:	Huaquan Wei Yanming Wang Yangming Li

Institution:	Department of Mathematics, Zhongshan University, Guangzhou 510275, China and Department of Mathematics, Guangxi Teacher's College, Nanning, 530001, China ; Lingnan College and Department of Mathematics, Zhongshan University, Guangzhou, 510275, China ; Department of Mathematics, Guangdong College of Education, Guangzhou, 510310, China

Abstract:	This paper proves: Let ${\cal F}$ be a saturated formation containing ${\cal U}$ . Suppose that is a group with a normal subgroup such that $G/H \in {\cal F}$ . (1) If all maximal subgroups of any Sylow subgroup of are -supple- mented in , then $G \in {\cal F}$ ; (2) If all minimal subgroups and all cyclic subgroups with order 4 of are -supplemented in , then $G \in {\cal F}$ .

Keywords:	$c$-supplemented subgroup supersolvable group the generalized Fitting subgroup saturated formation

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