On the solution of certain equations with exponent sum 0 over \(\mathbb{Z}_2\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 0989.20027
DOI: 10.1142/S0218196700000339
author: V. Ferlini
author: Richard Z. Goldstein
author: M. Salpukas
published in: International Journal of Algebra and Computation
publication date: 2002-04-15T00:00:00Z
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 20E05
zbMATH DE Number: 1587542
zbMATH Keywords: equations over groups
zbMATH Keywords: embeddings
zbMATH Keywords: exponent sums
zbMATH Keywords: dual relative diagrams
MaRDI profile type: Publication
cites work: Tesselations ofS2and equations over torsion-free groups
cites work: THE SOLUTION OF SETS OF EQUATIONS IN GROUPS
cites work: The solution of length three equations over groups
cites work: Solutions of equations over groups
cites work: Equations in groups
cites work: Adjunction of Elements To Groups
full work available at URL: s0218196700000339
OpenAlex ID: W2121606781
title: On the solution of certain equations with exponent sum 0 over \(\mathbb{Z}_2\)
review text: Let \(G\) be a group and \(t\) an unknown. Then a solution of an equation \(g_0t^{e(1)}g_1\cdots t^{e(n)}g_n=1\) in \(t\) over \(G\) is an embedding of \(G\) into a group \(H\), together with an element \(h\) of \(H\), such that \(g_0h^{e(1)}g_1\cdots h^{e(n)}g_n=1\) in \(H\). \(\sigma=e(1)+\cdots+e(n)\) is called the exponent sum. When \(\sigma=0\), nonsolvable examples are known [see \textit{R. C. Lyndon}, Bol. Soc. Bras. Math. 11, No. 1, 79-102 (1980; Zbl 0463.20030)].NEWLINENEWLINENEWLINEIn the paper under review the solvability of certain equations over \(\mathbb{Z}_2\) with exponent sum zero is examined. The equations are generalizations of the equation studied by Lyndon.
reviewed by: Brigitte Servatius
description: scientific article