Finite subgroups of groups of outer automorphisms of free groups
type: Item
instance of: scholarly article
title: Finite subgroups of groups of outer automorphisms of free groups
zbMATH Open document ID: 0657.20026
DOI: 10.1007/BF02009332
author: D. G. Khramtsov
published in: Algebra and Logic
publication date: 1987-01-01T00:00:00Z
review text: As it is shown by \textit{M. Culler} [Contemp. Math. 33, 197-207 (1984; Zbl 0552.20024)] any finite group of outer automorphisms \(K\leq Out F_ n\) of a free group \(F_ n\) (n finite) is realized by a group of homomorphisms of a graph. The author continues his investigations on finite groups of automorphisms initiated by him for \(L\leq Aut F_ n\) [in Mat. Zametki 38, No.3, 386-392 (1985; Zbl 0595.20036)] and proves that the group Out \(F_ n\) besides of projections of finite subgroups \(L\leq Aut F_ n\) contains only groups of automorphisms of regular cubic graphs with 2(n-1) vertices and also the subgroups of the group \(S_ 2\times S_{n+1}\). A description of possible orders of elements in Out \(F_ n\) is given. An algorithmical criterion of embedding any finite group K in the group Out \(F_ n\) is proposed.
Mathematics Subject Classification ID: 20F28
Mathematics Subject Classification ID: 20E05
zbMATH DE Number: 4073279
zbMATH Keywords: finite group of outer automorphisms
zbMATH Keywords: free group
zbMATH Keywords: regular cubic graphs
reviewed by: Vitaliĭ Roman'kov
MaRDI profile type: Publication
cites work: Finite groups of automorphisms of free groups
cites work: Q3344126
cites work: Finite and infinite cyclic extensions of free groups
description: scientific article; zbMATH DE number 4073279