Twisted conjugacy classes in special and general linear groups

Abstract

In this paper we study twisted conjugacy classes and the $R_{\infty }$-property for classical linear groups. In particular, we prove that the general linear group ${\mathrm{GL}}_n(K)$ and the special linear group ${\mathrm{SL}}_n(K)$ possess $R_{\infty }$-property, if $n\ge 3$ and $K$ is an infinite integral domain with trivial group of automorphisms (Theorem 1), or $K$ is an integral domain, which has a zero characteristic and for which $\mathrm{Aut}(K)$ is torsion (Theorem 2).

10 pages

References in corpus (1)

• On the Reidemeister spectrum and the $R_{\infty }$ property for some free nilpotent groups

Cited by in corpus (1)

• Twisted conjugacy classes in residually finite groups