Groups with pronormal deviation
type: Item
instance of: scholarly article
title: Groups with pronormal deviation
author: F. de Giovanni
author: Alessio Russo
author: L. A. Kurdachenko
published in: Journal of Algebra
publication date: 2022-10-18T00:00:00Z
review text: A subgroup \(X\) of a group \(G\) is said to be pronormal if \(X\) and \(X^{g}\) are conjugate in \(\langle X, X^{g} \rangle\) for every element \(g\in G\). Normal subgroups and maximal subgroups are obvious examples of pronormal subgroups in arbitrary groups; moreover, Sylow subgroups of finite groups and Hall subgroups of finite soluble groups are always pronormal. The main result proved in this article is the following Theorem: Let \(G\) be a radical group with pronormal deviation. Then either \(G\) is minimax or all its subgroups are pronormal. In particular, the pronormal deviation of \(G\) is at most 1. (An explanation of the technical terms can be found in the paper.)
reviewed by: Enrico Jabara
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F22
zbMATH DE Number: 7603201
zbMATH Keywords: pronormal subgroup
zbMATH Keywords: pronormal deviation
zbMATH Keywords: minimax group
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2022.09.007
OpenAlex ID: W4296675504
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DOI: 10.1016/J.JALGEBRA.2022.09.007
description: scientific article; zbMATH DE number 7603201