Subdirect products of finite groups with Hall \(\pi\)-subgroups
type: Item
instance of: scholarly article
title: Subdirect products of finite groups with Hall \(\pi\)-subgroups
zbMATH Open document ID: 0871.20015
DOI: 10.1007/BF02310964
author: V. A. Vedernikov
published in: Mathematical Notes
publication date: 1997-07-14T00:00:00Z
review text: Let \(\pi\) be a nonempty set of primes, and let \(E_\pi\) be the class of all finite groups that have Hall \(\pi\)-subgroups. A group that belongs to the class \(E_\pi\) is called an \(E_\pi\)-group. L. A. Shemetkov posed the following question: Is the class \(E_\pi\) closed under finite subdirect products? In the present note we answer this question in the affirmative under the condition that the Schreier conjecture on the solvability of the outer automorphism group of a finite simple group is valid.
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D40
zbMATH DE Number: 1028509
zbMATH Keywords: finite groups
zbMATH Keywords: Hall \(\pi\)-subgroups
zbMATH Keywords: subdirect products
MaRDI profile type: Publication
cites work: Theorems Like Sylow's
cites work: Q3961010
cites work: On the existence of Hall subgroups
cites work: Q3941595
cites work: Maximal subgroups of finite groups
description: scientific article; zbMATH DE number 1028509