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Bibliographic Details
Main Authors:	Andrew, Naomi, Conder, Matthew J., Markowitz, Ari, Schillewaert, Jeroen
Format:	Preprint
Published:	2024
Subjects:	Group Theory Number Theory 20G25 (Primary) 20E08 (Secondary)
Online Access:	https://arxiv.org/abs/2401.05192
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Table of Contents:

Let $K$ be a non-archimedean local field. We show that discrete subgroups without 2-torsion in $\mathrm{PSL}_2(K)$ can always be lifted to $\mathrm{SL}_2(K)$, and provide examples (when $\mathrm{char}(K) \neq 2$) which cannot be lifted if either of these conditions is removed. We also briefly discuss lifting representations of groups into $\mathrm{PSL}_2(K)$ to $\mathrm{SL}_2(K)$.