Ad~$(G)$ is of type $R$ implies $G$ is of type $R$ for certain $p$-adic Lie groups

TL;DR

This paper establishes a sufficient condition under which a $p$-adic Lie group inherits the type $R$ property from its adjoint image, contributing to the understanding of the structure of such groups.

Contribution

It introduces a new criterion linking the type $R$ property of a $p$-adic Lie group to that of its adjoint image, expanding the theoretical framework.

Findings

A sufficient condition for $p$-adic Lie groups to be of type $R$

Extension of type $R$ properties from adjoint images to groups

Enhanced understanding of the structure of $p$-adic Lie groups

Abstract

We provide a sufficient condition for a $p$-adic Lie group to be of type $R$ when its adjoint image is of type $R$.