具有$s$-可置换嵌入和弱$s$-可置换子群的有限群

Q4 Mathematics

Confluentes Mathematici Pub Date : 2013-01-01 DOI:10.5802/cml.4

Fenfang Xie, Jinjin Wang, Jiayi Xia, Guolei Zhong

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引用次数: 0

摘要

设G是一个有限群，p是G的最小素数，p是G的Sylow p-子群，产生子数d最小。存在p的极大子群的集合Md(p) = {P1, P2，···，Pd}，使得 di =1 Pi = Φ(p)。本文研究了一个有限群的结构，假设md (P)的每一个元素在G中要么是s置换嵌入的，要么是弱s置换的，给出了群是P超可解或P幂零的判据。

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Finite Groups with some $s$-Permutably Embedded and Weakly $s$-Permutable Subgroups

Let G be a finite group, p the smallest prime dividing the order of G and P a Sylow p-subgroup of G with the smallest generator number d. There is a set Md(P ) = {P1, P2, · · · , Pd} of maximal subgroups of P such that ⋂d i=1 Pi = Φ(P ). In the present paper, we investigate the structure of a finite group under the assumption that every member ofMd(P ) is either s-permutably embedded or weakly s-permutable in G to give criteria for a group to be p-supersolvable or p-nilpotent.

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来源期刊

Confluentes Mathematici Mathematics-Mathematics (miscellaneous)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Confluentes Mathematici is a mathematical research journal. Since its creation in 2009 by the Institut Camille Jordan UMR 5208 and the Unité de Mathématiques Pures et Appliquées UMR 5669 of the Université de Lyon, it reflects the wish of the mathematical community of Lyon—Saint-Étienne to participate in the new forms of scientific edittion. The journal is electronic only, fully open acces and without author charges. The journal aims to publish high quality mathematical research articles in English, French or German. All domains of Mathematics (pure and applied) and Mathematical Physics will be considered, as well as the History of Mathematics. Confluentes Mathematici also publishes survey articles. Authors are asked to pay particular attention to the expository style of their article, in order to be understood by all the communities concerned.