Twisted conjugacy classes in general and special linear groups.
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.
scientific article; zbMATH DE number 6121537
scientific article