Basis-conjugating automorphisms of a free group
type: Item
instance of: scholarly article
title: Basis-conjugating automorphisms of a free group
zbMATH Open document ID: 0913.20026
author: A. G. Savushkina
published in: Moscow University Mathematics Bulletin
publication date: 1998-03-29T00:00:00Z
review text: The paper extends the investigations undertook by the author in an earlier paper [Vestn. Mosk. Univ., Ser. I 1996, No. 1, 32-36 (1996; Zbl 0881.70002)]. In this paper it is proved that the group \({\mathfrak M}_n\) is a semidirect product of the (normal) subgroup \({\mathfrak C}_n\) and the subgroup \({\mathfrak M}_{n-1}\). Also it is shown that the group \({\mathfrak C}_n\) is the centralizer of the group \({\mathfrak M}_{n-1}\) in the group \({\mathfrak M}_n\) and in the group \({\mathfrak M}_n\) the centralizer of the group \({\mathfrak N}_n\) coincides with the centre of the group \({\mathfrak N}_n\) when \(n>2\).
Mathematics Subject Classification ID: 20F28
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 20F36
zbMATH DE Number: 1134954
zbMATH Keywords: semidirect products
zbMATH Keywords: centralizers
zbMATH Keywords: basis-conjugating automorphisms
zbMATH Keywords: free groups
zbMATH Keywords: pure braid groups
MaRDI profile type: Publication
Recommended article: On Basis-Conjugating Automorphisms of Free Groups
Recommended article: Q5457885
Recommended article: On the basis-conjugating automorphism groups of free groups and free metabelian groups
Recommended article: On the group of conjugating automorphisms of a free group
Recommended article: Normal Forms for Basis-Conjugating Automorphisms of a Free Group
Recommended article: Automorphisms of Free Groups
Recommended article: Automorphisms of automorphism groups of free groups
Recommended article: On automorphisms of free groups
Recommended article: Automorphisms of finitely generated free \(G\)-groups
Recommended article: Automorphisms of free groups and their fixed points
description: scientific article; zbMATH DE number 1134954