On recognizing the finite simple groups \(L_2(2^m)\) in the class of all groups
type: Item
instance of: scholarly article
title: On recognizing the finite simple groups \(L_2(2^m)\) in the class of all groups
zbMATH Open document ID: 0941.20010
DOI: 10.1007/BF02674291
published in: Siberian Mathematical Journal
publication date: 2000-04-16T00:00:00Z
review text: Given a group \(G\), let \(\omega(G)\) be the set of all orders of the elements of \(G\). Let \(L_2(q)=\text{PSL}_2(q)\) be the projective special linear group of dimension 2 over the finite field of order \(q=2^m\). Theorem. Let \(G\) be a group and let \(\omega(G)=\omega(L_2(q))\), \(q=2^m>2\). Then \(G\) is isomorphic to \(L_2(q)\). This theorem generalizes a theorem by \textit{W.~Shi} [Adv. Math., Beijing 16, 397-401 (1987; Zbl 0643.20008)].
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 1432165
zbMATH Keywords: orders of elements
zbMATH Keywords: finite simple groups
zbMATH Keywords: involutions
author: A. Kh. Zhurtov
author: V. D. Mazurov
MaRDI profile type: Publication
cites work: Q3785024
cites work: A characterization of the one-dimensional unimodular projective groups over finite fields
cites work: Q5621472
description: scientific article; zbMATH DE number 1432165