Two properties of the filtration of the outer automorphism groups of certain groups
type: Item
instance of: scholarly article
title: Two properties of the filtration of the outer automorphism groups of certain groups
zbMATH Open document ID: 0814.20026
DOI: 10.1007/BF02571892
author: Mamoru Asada
published in: Mathematische Zeitschrift
publication date: 1995-06-18T00:00:00Z
full work available at URL: https://eudml.org/doc/174717
review text: Let \(G\) be a finitely generated discrete or pro-\(\ell\)-group, \(\ell\) being a fixed prime number. Let \(\Gamma\) denote the outer automorphism group of \(G\). The group \(\Gamma\) has a filtration \(\{\Gamma[m]\}_{m \geq 0}\) which is naturally induced from the descending central series of \(G\). We shall show, under some assumptions on \(G\), that the abelian group \(\Gamma[m]/\Gamma[m+1]\) (\(m \geq 1\)) is a free \(Z\) (or \(Z_ \ell\))- module of finite rank and that the intersection \(\bigcap^ \infty_{m = 0} \Gamma[m]\) reduces to \(\{1\}\) (in the pro-\(\ell\) case).
Mathematics Subject Classification ID: 20F28
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 20E18
Mathematics Subject Classification ID: 20C07
zbMATH DE Number: 737164
zbMATH Keywords: finitely generated group
zbMATH Keywords: pro-\(\ell\)-group
zbMATH Keywords: outer automorphism group
zbMATH Keywords: filtration
zbMATH Keywords: descending central series
MaRDI profile type: Publication
cites work: Exactness properties of profinite completion functors
cites work: On the Automorphisms of Free Groups and Free Nilpotent Groups
cites work: Q3804906
cites work: On generalised free products
cites work: The centre of groups with one defining relator
cites work: Q5655596
cites work: On the Residual Finiteness of Certain Mapping Class Groups
cites work: Q3808200
cites work: Q3211418
cites work: On the descending central series of groups with a single defining relation
cites work: Combinatorial group theory for pro-p groups
cites work: Q4145882
cites work: Über Beziehungen zwischen höheren Kommutatoren.
cites work: The center of a group with a single defining relation
OpenAlex ID: W2086624417
description: scientific article; zbMATH DE number 737164