A Characteristic Subgroup of an Enπ Group

A Characteristic Subgroup of an Enπ Group

Yangming Li;Yanming Wang

【期刊名称】《代数集刊（英文版）》 【年(卷),期】2005(012)002

【摘要】. Suppose G is a group which is p-stable and p-constrained, where p is an odd prime, and S is a Sylow p-subgroup of G. A classical theorem of Glauberman shows that ZJ(S)Op′ (G) △G, whereJ(S) is the Thompson subgroup of S. In this paper, we generalize the above result by replacing the odd prime p with a set π of odd primes. More precisely,suppose π is a set of odd primes and G is an Enπ group which is π-stable and π-constrained.We prove that if H ∈ Hallπ (G), then ZJ(H)Oπ′ (G)△ G and G = NG(ZJ(H))Oπ′ (G). An interesting application is also given.

【总页数】10页(309-318)

【关键词】π-stable group;π-constrained group;Hall subgroup;the generalized Thompson subgroup 【作者】Yangming Li;Yanming Wang

【作者单位】Department of Mathematics, Zhejiang University, Hangzhou 310028, China;Department of Mathematics, Guangdong College of Education Guangzhou 510310, China;Lingnan College and School of Mathematics Zhongshan University, Guangzhou 510275, China

【正文语种】中文 【中图分类】 【相关文献】

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