Illinois Journal of Mathematics

On $\mathcal{M}$-permutable sylow subgroups of finite groups

Long Miao and Wolfgang Lempken

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Abstract

A $p$-subgroup $P\neq 1$ of $G$ is called $\mathcal{M}$-permutable in $G$ if there exists a set $\mathcal{ M}_d(P)=\{P_1,\ldots,P_d\}$ of maximal subgroup $P_i$ of $P$ and a subgroup $B$ of $G$ such that: (1) $\bigcap_{i=1}^{d}{P_i}=\Phi(P)$ and $|P : \Phi(P)|=p^d$; (2) $G=PB$ and $P_iB=BP_i \lt G$ for any $P_i$ of $\mathcal{M}_d(P)$. In this paper, we investigate the influence of $\mathcal M$-permutability of Sylow subgroups in finite groups. Some new results about supersolvable groups and formations are obtained.

Article information

Source
Illinois J. Math., Volume 53, Number 4 (2009), 1095-1107.

Dates
First available in Project Euclid: 22 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1290435341

Digital Object Identifier
doi:10.1215/ijm/1290435341

Mathematical Reviews number (MathSciNet)
MR2741180

Zentralblatt MATH identifier
1214.20022

Subjects
Primary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $\pi$-length, ranks [See also 20F17] 20D20: Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure

Citation

Miao, Long; Lempken, Wolfgang. On $\mathcal{M}$-permutable sylow subgroups of finite groups. Illinois J. Math. 53 (2009), no. 4, 1095--1107. doi:10.1215/ijm/1290435341. https://projecteuclid.org/euclid.ijm/1290435341


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