Factorization of group homomorphisms
type: Item
instance of: scholarly article
title: Factorization of group homomorphisms
zbMATH Open document ID: 1006.20024
DOI: 10.1016/S0022-4049(01)00122-0
published in: Journal of Pure and Applied Algebra
publication date: 2002-08-22T00:00:00Z
review text: The authors show that if \(\pi\) is a (torsion-free) virtually polycyclic group, then for any finitely generated group \(G\) there exists a (torsion-free) virtually polycyclic group \(\overline G\) and an epimorphism \(\varepsilon_G\colon G\to\overline G\) such that every homomorphism \(\varphi\colon G\to\pi\) factors into \(\varphi=\overline\varphi\circ\varepsilon_G\) for some homomorphism \(\overline\varphi\colon\overline G\to\pi\). This unique factorization property is applied to obtain conditions for which the Nielsen coincidence number \(N(f,g)\) and the Reidemeister coincidence number \(R(f,g)\) coincide for maps \(f,g\colon X\to Y\) into an infra-solvmanifold \(Y\).
reviewed by: Wim Malfait
Mathematics Subject Classification ID: 20E10
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 20E36
zbMATH DE Number: 1787448
zbMATH Keywords: torsion-free virtually polycyclic groups
zbMATH Keywords: infrasolvmanifolds
zbMATH Keywords: coincidences of two maps
zbMATH Keywords: homomorphisms
author: Daciberg Lima Gonçalves
author: Peter Wong
MaRDI profile type: Publication
cites work: Rigidity and other topological aspects of compact nonpositively curved manifolds
cites work: Generalized classes of groups, $C$-nilpotent spaces and "The Hurewicz theorem".
cites work: Q4244970
cites work: Nilmanifolds are Jiang-type spaces for coincidences
cites work: Q4086427
cites work: Q4110334
cites work: Maps on infra-nilmanifolds. Rigidity and applications to fixed-point theory
cites work: Varieties of groups
cites work: Groupes d'homotopie et classes de groupes abéliens
cites work: A Residual Property of Certain Linear Groups
description: scientific article; zbMATH DE number 1787448