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In this paper we study twisted conjugacy classes and the$R_{\infty}$-property for classical linear groups. In particular, we prove thatthe general linear group ${\rm GL}_n(K)$ and the special linear group ${\rmSL}_n(K)$ possess $R_{\infty}$-property, if $n\geq3$ and $K$ is an infiniteintegral domain with trivial group of automorphisms (Theorem 1), or $K$ is anintegral domain, which has a zero characteristic and for which ${\rm Aut}(K)$is torsion (Theorem 2).

Twisted conjugacy classes in special and general linear groups