T. Nasybullov
Published 2019-07-04Version 1
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.
Comments: 17 pages. arXiv admin note: text overlap with arXiv:1708.06280
$R_{\infty}$ property for Chevalley groups of types $B_l, C_l, D_l$ over integral domains
On the Conjugacy Classes in the orthogonal and symplectic groups over algebraically closed fields
On the $\mathbb{A}^1$-invariance of $\mathrm{K}_2$ of Chevalley groups of simply-laced type
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