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

TL;DR

This paper proves that classical Chevalley groups over certain rings in characteristic p>0 possess the $R_{ ext{infinity}}$-property, indicating infinite twisted conjugacy classes under automorphisms.

Contribution

It establishes the $R_{ ext{infinity}}$-property for classical Chevalley groups over a broad class of rings in characteristic p>0, extending previous results.

Findings

Classical Chevalley groups over specified rings have the $R_{ ext{infinity}}$-property.

The result applies to rings between a subfield of algebraic closure of finite fields and their rational function fields.

The proof covers groups over rings in characteristic p>0, excluding p=2.

Abstract

Let $F$ be a subfield of the algebraic closure of a finite field $\mathbb{F}_p$, $p \ne 2$, and let $R$ denote any ring such that $F[t] \subset R \subsetneq F(t)$. Let $G$ be a classical Chevalley group of adjoint type defined over $R$. We prove that the group $G(R)$ has the $R_{\infty}$-property.