A conjecture of Frobenius and the simple groups of Lie type. IV
type: Item
instance of: scholarly article
title: A conjecture of Frobenius and the simple groups of Lie type. IV
zbMATH Open document ID: 0814.20019
author: N. Iiyori
published in: Journal of Algebra
publication date: 1993-03-29T00:00:00Z
review text: Let \(G\) be a finite group, \(e\) be a positive integer dividing \(| G|\) and \(L_ e(G) = \{x \in G \mid x^ e = 1\}\). Frobenius showed that \(| L_ e(G)| \equiv 0 \pmod e\) and conjectured that \(L_ e(G)\) forms a subgroup provided \(e = | L_ e(G)|\). This paper is one in the series of articles which proves the Frobenius conjecture modulo the classification of the finite simple groups [for part III, cf. the author and \textit{H. Yamaki}, ibid. 145, No. 2, 329-332 (1992; Zbl 0745.20014)]. Indeed, the author proves that the Frobenius conjecture is true for the simple groups \(B_ n(q)\), \(D_ n(q)\), \(^ 2 A_ n(q)\) and \(^ 2 D_ n(q)\).
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D06
zbMATH DE Number: 130516
zbMATH Keywords: finite group
zbMATH Keywords: Frobenius conjecture
zbMATH Keywords: classification of the finite simple groups
Wikidata QID: Q115396334
reviewed by: V. D. Mazurov
MaRDI profile type: Publication
full work available at URL: jabr.1993.1011
OpenAlex ID: W4213338478
DOI: 10.1006/JABR.1993.1011
description: scientific article; zbMATH DE number 130516