Translator Disclaimer
July 2016 Partially ordered sets of non-trivial nilpotent $\pi$-subgroups
Nobuo Iiyori, Masato Sawabe
Osaka J. Math. 53(3): 731-750 (July 2016).

Abstract

In this paper, we introduce a subposet $\mathcal{L}_{\pi}(G)$ of a poset $\mathcal{N}_{\pi}(G)$ of all non-trivial nilpotent $\pi$-subgroups of a finite group $G$. We examine basic properties of subgroups in $\mathcal{L}_{\pi}(G)$ which contain the notion of both radical $p$-subgroups and centric $p$-subgroups of $G$. It is shown that $\mathcal{L}_{\pi}(G)$ is homotopy equivalent to $\mathcal{N}_{\pi}(G)$. As examples, we investigate in detail the case where symmetric groups.

Citation

Download Citation

Nobuo Iiyori. Masato Sawabe. "Partially ordered sets of non-trivial nilpotent $\pi$-subgroups." Osaka J. Math. 53 (3) 731 - 750, July 2016.

Information

Published: July 2016
First available in Project Euclid: 5 August 2016

zbMATH: 1358.20015
MathSciNet: MR3533466

Subjects:
Primary: 20E15
Secondary: 20D15

Rights: Copyright © 2016 Osaka University and Osaka City University, Departments of Mathematics

JOURNAL ARTICLE
20 PAGES


SHARE
Vol.53 • No. 3 • July 2016
Back to Top