Finite groups of outer automorphisms of free groups
type: Item
instance of: scholarly article
title: Finite groups of outer automorphisms of free groups
zbMATH Open document ID: 0792.20023
DOI: 10.1007/BF00971178
published in: Siberian Mathematical Journal
publication date: 1992-09-26T00:00:00Z
review text: In 1989 V. D. Mazurov and D. G. Khramtsov have completed the classification of finite groups of outer automorphisms of a finitely generated free group \(F_ n\) in relation to its rank \(n\) up to isomorphism. The list of such groups consists of 1) all subgroups of direct products \(H_ \nu = \prod^ s_{i = 1} (S_{m_ i}\wr_ \pi S_{k_ i})\) of permutation wreath products \(S_{m_ i}\wr_ \pi S_{k_ i}\) of symmetric groups \(S_{m_ i}\) and \(S_{k_ i}\) for any set \(\nu\) of integers \(m_ i \geq 2\), \(k_ i \geq 1\), \(i = 1,\dots,s\), satisfying \(\sum^ s_{i = 1}(m_ i - 1)k_ i \leq n\), 2) all subgroups of \(S_{n+1} \times Z_ 2\), 3) two exceptional subgroups for \(n = 10\). The proof of this result depended on parts of the classification of finite simple groups (CFSG). The paper under review eliminates this problem by giving a proof independent of CSFG.
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 20F28
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 56506
zbMATH Keywords: finite groups of outer automorphisms
zbMATH Keywords: finitely generated free group
zbMATH Keywords: permutation wreath products
zbMATH Keywords: classification of finite simple groups
author: V. D. Mazurov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 56506