  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 ${\rm GL}_n(K)$ and the special linear group ${\rm
SL}_n(K)$ possess $R_{\infty}$-property, if $n\geq3$ 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 ${\rm Aut}(K)$
is torsion (Theorem 2).

Group Theory