$The Hall property $\mathcal{D}_\pi$ is inherited by overgroups of $\pi$-Hall subgroups$

The Hall property $\mathcal{D}_\pi$ is inherited by overgroups of $\pi$-Hall subgroups

Let $\pi$ be a set of primes. We say that a finite group $G$ is a $\mathcal{D}_\pi$-group if the maximal $\pi$-subgroups of $G$ are conjugate. In this paper, we give an affirmative answer to Problem 17.44(b) from "Kourovka notebook", namely we prove that in a $\mathcal{D}_\pi$-...

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Veröffentlicht in:	arXiv.org 2018-08
Hauptverfasser:	Nomina Ch Manzaeva, Revin, Danila O, Vdovin, Evgeny P
Format:	Artikel
Sprache:	eng
Schlagworte:	Subgroups
Online-Zugang:	Volltext
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Zusammenfassung:	Let $\pi$ be a set of primes. We say that a finite group $G$ is a $\mathcal{D}_\pi$-group if the maximal $\pi$-subgroups of $G$ are conjugate. In this paper, we give an affirmative answer to Problem 17.44(b) from "Kourovka notebook", namely we prove that in a $\mathcal{D}_\pi$-group an overgroup of a $\pi$-Hall subgroup is always a $\mathcal{D}_\pi$-group.
ISSN:	2331-8422
DOI:	10.48550/arxiv.1808.03536

Zusammenfassung:	Let \(\pi\) be a set of primes. We say that a finite group \(G\) is a \(\mathcal{D}_\pi\)-group if the maximal \(\pi\)-subgroups of \(G\) are conjugate. In this paper, we give an affirmative answer to Problem 17.44(b) from "Kourovka notebook", namely we prove that in a \(\mathcal{D}_\pi\)-group an overgroup of a \(\pi\)-Hall subgroup is always a \(\mathcal{D}_\pi\)-group.
ISSN:	2331-8422
DOI:	10.48550/arxiv.1808.03536

The Hall property \(\mathcal{D}_\pi\) is inherited by overgroups of \(\pi\)-Hall subgroups