Chevalley groups of types $B_n$, $C_n$, $D_n$ over certain fields do not possess the $R_{\infty}$-property

Abstract

Let F be an algebraically closed field of zero characteristic. If the transcendence degree of F over Q is finite, then all Chevalley groups over F are known to possess the R ∞ -property. If the transcendence degree of F over Q is infinite, then Chevalley groups of type A n over F do not possess the R ∞property. In the present paper we consider Chevalley groups of classical series B n , C n , D n over F in the case when the transcendence degree of F over Q is infinite, and prove that such groups do not possess the R ∞ -property.

Twisted conjugacy in $${\mathrm {GL}}_2$$ and $${\mathrm {SL}}_2$$ over polynomial algebras over finite fields

“…In this paper we address this question for the class of general and special linear groups over polynomial and Laurent polynomial algebras over a field F which is a subfield of the algebraic closure of F p . The same question for linear groups over fields of characteristic zero was considered by Nasybullov [15], [16] and Felshtyn and Nasybullov [4] culminating in the result that a Chevally group of classical type over an algebraically closed field F of characteristic zero has the R ∞ -property if and only if F has finite transcendence degree over Q.…”