Twisted conjugacy classes in special and general linear groups
T. R.Nasybullov

TL;DR
This paper investigates twisted conjugacy classes and the $R_{ty}$-property in classical linear groups, establishing conditions under which these groups exhibit this property.
Contribution
It proves that ${ m GL}_n(K)$ and ${ m SL}_n(K)$ have the $R_{ty}$-property for certain types of integral domains and dimensions.
Findings
${ m GL}_n(K)$ and ${ m SL}_n(K)$ possess $R_{ty}$-property for $n \\geq 3$
The property holds when $K$ has trivial automorphism group
The property also holds when $K$ has zero characteristic and torsion automorphism group
Abstract
In this paper we study twisted conjugacy classes and the -property for classical linear groups. In particular, we prove that the general linear group and the special linear group possess -property, if and is an infinite integral domain with trivial group of automorphisms (Theorem 1), or is an integral domain, which has a zero characteristic and for which is torsion (Theorem 2).
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Taxonomy
TopicsGeometric and Algebraic Topology · Finite Group Theory Research · Advanced Algebra and Geometry
