Twisted conjugacy classes in Chevalley groups

Abstract

We prove that Chevalley group over the field $F$ of zero characteristic possess $R_{\infty }$ property, if $F$ has torsion group of automorphisms or $F$ is an algebraically closed field which has finite transcendence degree over $\mathbb{Q}$. As a consequence we obtain that the twisted conjugacy class $[e{]}_{\phi }$ of unit element is a subgroup of Chevalley group if and only if $\phi$ is central automorphism.

arXiv comment24 pages, 2 figures