Twisted conjugacy classes in twisted Chevalley groups

Abstract

Let G be a group and ϕ be an automorphism of G. Two elements x, y of G are said to be ϕ-twisted if y = gxϕ(g)^{-1} for some g in G. We say that a group G has the R_{\infty}-property if the number of ϕ-twisted conjugacy classes is infinite for every automorphism ϕ of G. In this paper, we prove that twisted Chevalley groups over the field k of characteristic zero have the R_{\infty}-property as well as S_{\infty}-property if k has finite transcendence degree over \mathbb{Q} or Aut(k) is periodic.

18 pages. Final version to appear in Journal of Algebra and its Applications