On finite simple groups with the set of element orders as in a Frobenius group or a double Frobenius group.
type: Item
instance of: scholarly article
title: On finite simple groups with the set of element orders as in a Frobenius group or a double Frobenius group.
zbMATH Open document ID: 1065.20025
DOI: 10.1023/A:1023253609066
author: M. R. Aleeva
published in: Mathematical Notes
publication date: 2004-11-15T00:00:00Z
review text: Using the classification, it is proved that the only finite simple groups having the same element orders as a Frobenius group are \(L_3(3)\) and \(U_3(3)\). Examples of corresponding Frobenius groups are specific groups of shape \(13^2:2S^-_4\) and \(7^4:3:8\), respectively. Similarly, the only possible finite simple groups having the same element orders as a double Frobenius group (a group of shape \(A:B:C\) where \(A:B\) and \(B:C\) are Frobenius groups) are \(U_3(3)\) and \(S_4(3)\). No double Frobenius groups with these sets of element orders are apparently known.
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 2115570
zbMATH Keywords: finite simple groups
zbMATH Keywords: double Frobenius groups
zbMATH Keywords: sets of element orders
reviewed by: Robert A. Wilson
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2115570