On 9- and 10-decomposable finite groups.
type: Item
instance of: scholarly article
title: On 9- and 10-decomposable finite groups.
zbMATH Open document ID: 1157.20007
author: Shi Wujie
author: A. R. Ashrafi
published in: Journal of Applied Mathematics and Computing
publication date: 2008-10-21T00:00:00Z
full work available at URL: http://hdl.handle.net/10338.dmlcz/131538
review text: A finite group is called \(n\)-decomposable if every proper non-trivial normal subgroup of \(G\) is a union of \(n\) distinct conjugacy classes of \(G\). The first author with co-authors studied the question of finding all positive integers \(n\) such that there is an \(n\)-decomposable finite group. In this paper, the authors describe 9- and 10-decomposable non-perfect finite groups. They prove that a non-perfect finite group \(G\) is 9-decomposable if and only if \(G\) is isomorphic to \(\Aut(L_2(32))\), \(\Aut(L_3(3))\), the non-Abelian semi-direct product \((Z_5\times Z_5):Z_3\) or a non-Abelian group of order \(pq\), where \(p\) and \(q\) are primes and \(p-1=8q\), and also a non-perfect finite group \(G\) is 10-decomposable if and only if \(G\) is isomorphic to \(\Aut(L_2(17))\), \(L_2(25):2_3\), \(\Aut(U_3(3))\) or the dihedral group of order 38.
reviewed by: Anatoli Kondrat'ev
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20E45
Mathematics Subject Classification ID: 20E34
zbMATH DE Number: 5354594
zbMATH Keywords: normal subgroups
zbMATH Keywords: unions of conjugacy classes
zbMATH Keywords: \(n\)-decomposable groups
zbMATH Keywords: non-perfect finite groups
Wikidata QID: Q61987938
describes a project that uses: GAP
MaRDI profile type: Publication
OpenAlex ID: W2109530731
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DOI: 10.1007/S12190-007-0001-8
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description: scientific article; zbMATH DE number 5354594