Sur un problème au sujet des homomorphismes. (On a problem concerning homomorphisms)
type: Item
instance of: scholarly article
title: Sur un problème au sujet des homomorphismes. (On a problem concerning homomorphisms)
zbMATH Open document ID: 0637.39005
DOI: 10.1007/BF02311317
author: Zenon Moszner
published in: Aequationes Mathematicae
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137193
review text: Let f and g be homomorphisms from the additive group \((R,+)\) into a group (G,\(\cdot)\). The author considers the problem, when the relation \((1)\quad \bigwedge_{t\in R}f(t)g(t)=g(t)f(t)\) implies the condition \((2)\quad \bigwedge_{t,s\in R}f(t)g(s)=g(s)f(t).\) The author gives some conditions for homomorphisms f,g and group G which ensure the above implication. Moreover it is given an example of a group G, with the following property: for every linear subspace P of R over Q with codim \(P\geq 2\), there exist homomorphisms f and g from \((R,+)\) into (G,\(\cdot)\) satisfying (1) and \(\bigvee_{s,t\in R}f(s)g(t)\neq g(t)f(s)\) and Ker f\(=Ker g=P\).
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 20F99
zbMATH DE Number: 4038394
zbMATH Keywords: iteration group
zbMATH Keywords: topological group
zbMATH Keywords: Hamel basis
zbMATH Keywords: matrix
zbMATH Keywords: homomorphisms
reviewed by: Marek Cezary Zdun
MaRDI profile type: Publication
cites work: Über die multiplikative Cauchysche Funktionalgleichung für Matrizen dritter Ordnung
cites work: Q5577573
cites work: Quelques remarques sur l'équation fonctionnelle matricielle multiplicative de Cauchy
cites work: The matrix equation \(a(x\cdot y)=a(x)+a(x)a(y)+a(y)\)
cites work: Equations of the form \(H(x\cdot y)=\sum_if_i(x)g_i(y)\)
cites work: Q3488618
description: scientific article; zbMATH DE number 4038394