How far are p-adic Lie groups from algebraic groups?

TL;DR

This paper investigates the structure of weakly regular p-adic Lie groups, demonstrating that the subgroup generated by one-parameter subgroups admits a Levi decomposition and identifying a regular open subgroup containing it.

Contribution

It establishes a Levi decomposition for the subgroup generated by one-parameter subgroups in weakly regular p-adic Lie groups and finds a regular open subgroup containing this subgroup.

Findings

Existence of a Levi decomposition for G_u

Identification of a regular open subgroup containing G_u

Structural insights into weakly regular p-adic Lie groups

Abstract

We show that, in a weakly regular $p$-adic Lie group $G$, the subgroup $G_u$ spanned by the one-parameter subgroups of $G$ admits a Levi decomposition. As a consequence, there exists a regular open subgroup of $G$ which contains $G_u$.