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

## TL;DR

This paper proves that Chevalley groups of types B, C, D over certain infinite transcendence degree fields do not have the $R_{ty}$-property, extending previous results known for other types.

## Contribution

It demonstrates that Chevalley groups of types B, C, D over fields with infinite transcendence degree lack the $R_{ty}$-property, filling a gap in the understanding of these groups.

## Key findings

- Chevalley groups of types B, C, D over fields with infinite transcendence degree do not possess the $R_{ty}$-property.
- The result extends known properties from other types to these classical series.
- The paper clarifies the behavior of automorphisms and twisted conjugacy classes in these groups.

## Abstract

Let $F$ be an algebraically closed field of zero characteristic. If the transcendence degree of $F$ over $\mathbb{Q}$ is finite, then all Chevalley groups over $F$ are known to possess the $R_{\infty}$-property. If the transcendence degree of $F$ over $\mathbb{Q}$ is infinite, then Chevalley groups of type $A_n$ over $F$ do not possess the $R_{\infty}$-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 $\mathbb{Q}$ is infinite, and prove that such groups do not possess the $R_{\infty}$-property.