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

Nomina Ch. Manzaeva; Danila O. Revin; Evgeny P. Vdovin

doi:10.1070/SM9185

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

Group Theory 2020-08-26 v1

Authors: Nomina Ch. Manzaeva , Danila O. Revin , Evgeny P. Vdovin

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Abstract

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.

Keywords

finite groups hall subgroups d_pi-groups conjugacy kourovka notebook

Cite

@article{arxiv.1808.03536,
  title  = {The Hall property $\mathcal{D}_\pi$ is inherited by overgroups of $\pi$-Hall subgroups},
  author = {Nomina Ch. Manzaeva and Danila O. Revin and Evgeny P. Vdovin},
  journal= {arXiv preprint arXiv:1808.03536},
  year   = {2020}
}

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arXiv admin note: text overlap with arXiv:1504.03137

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

Abstract

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