A characterization of finite simple groups by the orders of solvable subgroups.
type: Item
instance of: scholarly article
title: A characterization of finite simple groups by the orders of solvable subgroups.
zbMATH Open document ID: 1134.20008
author: Klaus Denecke
author: Xianhua Li
author: Jianxing Bi
published in: Science in China. Series A
publication date: 2007-09-10T00:00:00Z
review text: The authors prove that if a finite group \(G\) and a finite simple group \(S\) have the same sets of all orders of solvable subgroups, then \(G\) is isomorphic to \(S\), or \(G\) and \(S\) are isomorphic to \(B_n(q)\), \(C_n(q)\), where \(n\geq 3\) and \(q\) is odd. Since \textit{N. Ahanjideh} and \textit{A. Iranmanesh} prove a theorem on the difference of orders of solvable subgroups between \(B_n(q)\) and \(C_n(q)\) [On the difference between orders of solvable subgroups of the nonisomorphic simple groups \(B_n(q)\) and \(C_n(q)\) (manuscript)], the conjecture put forward by \textit{S. Abe} and \textit{N. Iiyori}, [Hokkaido Math. J. 29, No. 2, 391-407 (2000; Zbl 0965.20008)], is proved.
reviewed by: Shi Wujie
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 5189100
zbMATH Keywords: finite simple groups
zbMATH Keywords: orders of solvable subgroups
MaRDI profile type: Publication
full work available at URL: s11425-007-0024-5
OpenAlex ID: W1927433067
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DOI: 10.1007/S11425-007-0024-5
description: scientific article; zbMATH DE number 5189100