Are there free groups in division rings?
type: Item
instance of: scholarly article
title: Are there free groups in division rings?
zbMATH Open document ID: 0597.16017
DOI: 10.1007/BF02772670
author: Arnaldo Mandel
author: J. Z. Gonçalves
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The authors approach the following conjecture 1. Any noncentral subnormal subgroup of the multiplicative group \(D^*\) of a skew field D contains a free subgroup of rank two. They show that this conjecture holds in some special cases when the original skew field contains an appropriate finite dimensional skew field. They also investigate the following weaker conjecture 2. A word from a free group defines a substitution mapping of \(D^*\) to \(D^*\). The conjecture is that any such mapping cannot map a noncentral subnormal subgroup of \(D^*\) into the center of D. The authors provide several examples of words for which this conjecture is true.
Mathematics Subject Classification ID: 16Kxx
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 3961879
zbMATH Keywords: noncentral subnormal subgroup
zbMATH Keywords: multiplicative group
zbMATH Keywords: skew field
zbMATH Keywords: free subgroup
zbMATH Keywords: substitution mapping
reviewed by: Leonid Makar-Limanov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02772670
OpenAlex ID: W2049086652
description: scientific article; zbMATH DE number 3961879