$$\mathfrak{X}$$ - permutable subgrou ps and p-nil potency of finite grou ps II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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$$\mathfrak{X}$$ - permutable subgrou ps and p-nil potency of finite grou ps II

Authors:	Xianhua Li Yangming Li Lifang Wang

Institution:	(1) School of Mathematical Science, Suzhou University, Suzhou, 215006, China;(2) Department of Mathematics, Guangdong Institute of Education, Guangzhou, 510310, China;(3) School of Mathematics and Computer Science, Shanxi Normal University, Linfen, 041004, China

Abstract:	Let $\mathfrak{X}$ be a complete set of Sylow subgroups of a finite group G, that is, for each prime p dividing the order of G, $\mathfrak{X}$ contains one and only one Sylow p-subgroup of G. A subgroup H of G is said to be $\mathfrak{X}$ -permutable in G if H permutes with every member of $\mathfrak{X}$ . In this paper we characterize p-nilpotency of finite groups G; we will assume that some minimal subgroups or 2-minimal subgroups of G are $\mathfrak{X}$ -permutable in G. Moreover, the duals of some recent results are obtained. Supported by the NSF of China(10571128) and the NSF of Colleges and Suzhou City Senior Talent Supporting Project. Project supported in part by NSF of China (10571181), NSF of Guangdong Province (06023728) and ARF(GDEI). Project supported in part by the NSF for youth of Shanxi Province (2007021004) and TianYuan Fund of Mathematics of China (10726002).

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