Twisted conjugacy classes in general and special linear groups.
type: Item
instance of: scholarly article
title: Twisted conjugacy classes in general and special linear groups.
zbMATH Open document ID: 1264.20046
published in: Algebra and Logic
publication date: 2013-01-03T00:00:00Z
review text: The author considers twisted conjugacy classes and the \(R_\infty\)-property for classical linear groups. The property means that the number of \(\varphi\)-conjugacy classes is infinite for every automorphism \(\varphi\) of \(G\). In particular, it is stated that the general linear group \(\mathrm{GL}_n(K)\) and the special linear group \(\mathrm{SL}_n(K)\), where \(n\geqslant 3\), possess the \(R_\infty\)-property if either \(K\) is an infinite integral domain with trivial automorphism group or \(K\) is an integral domain containing a subring of integers, whose automorphism group \(\Aut(K)\) is finite. An integral domain is a commutative ring with identity which has no zero divisors.
Mathematics Subject Classification ID: 20G35
Mathematics Subject Classification ID: 20E45
Mathematics Subject Classification ID: 55M20
zbMATH DE Number: 6121537
zbMATH Keywords: general linear groups
zbMATH Keywords: special linear groups
zbMATH Keywords: numbers of twisted conjugacy classes
zbMATH Keywords: automorphism groups
zbMATH Keywords: integral domains
author: Timur Nasybullov
reviewed by: L. N. Vaserstein
MaRDI profile type: Publication
full work available at URL: s10469-012-9185-6
OpenAlex ID: W1984520673
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DOI: 10.1007/S10469-012-9185-6
description: scientific article; zbMATH DE number 6121537