D'Alembert's functional equations on metabelian groups
type: Item
instance of: scholarly article
title: D'Alembert's functional equations on metabelian groups
zbMATH Open document ID: 0959.39023
author: Henrik Stetkær
published in: Aequationes Mathematicae
publication date: 2001-04-19T00:00:00Z
review text: A group is metabelian if its commutator subgroup is contained in its centre. This paper offers the general solution, mapping a metabelian group \(G\) into the multiplicative group of the nonzero complex numbers, of the (generalized) d'Alembert equation \(g(xy)+g(xh(y))=2g(x)g(y)\), \(x,y\in G,\) where \(h\) is an involution of \(G.\) Also, the equation \(g(xy)+g(yx)+g(xh(y))+g(h(x)y)=4g(x)g(y)\), \(x,y\in G\), is reduced to the above d'Alembert equation.
reviewed by: János Aczél
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 1496062
zbMATH Keywords: d'Alembert's functional equations
zbMATH Keywords: metabelian group
zbMATH Keywords: commutator subgroup
zbMATH Keywords: centre
zbMATH Keywords: involution
MaRDI profile type: Publication
full work available at URL: s000100050130
OpenAlex ID: W2024966247
DOI: 10.1007/S000100050130
description: scientific article; zbMATH DE number 1496062