The R∞-property for Chevalley groups of types Bl,

Abstract

We prove that Chevalley groups of the classical series B l , C l , D l over an integral domain of zero characteristic, which has periodic automorphism group, possess the R ∞ -property.

Twisted conjugacy in direct products of groups

“…Theorem 3] that certain reductive linear algebraic groups G have the R ∞ -property by proving it for the quotient group G/R(G), which splits as a direct product of Chevalley groups. The latter can also be proved by combining the results from [32,33,34,35,36] with Corollary 4.5.…”

Twisted conjugacy in classical groups over certain domains of Characteristic $p>0$

“…Various other authors have studied R ∞ -property of linear groups. See [3], [13], [17], [18], [19], [20], [21]. Nasybullov [20] and Felshtyn-Nasybullov [3] proved that 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.…”

“…See [3], [13], [17], [18], [19], [20], [21]. Nasybullov [20] and Felshtyn-Nasybullov [3] proved that 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. It follows from a classical theorem by Steinberg [15] that any connected linear algebraic group over an algebraically closed field of characteristic p > 0 does not have the R ∞ -property.…”

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

“…The author studied conditions which imply the R ∞ -property for different linear groups over rings [11,13,15] and fields [5,12,14,15]. In particular, it was proved that if F is a field of zero characteristic which has either finite transcendence degree over Q, or periodic group of automorphisms, then every Chevalley group (of normal type) over F possesses the R ∞ -property [12].…”