How Far Are p-Adic Lie Groups from Algebraic Groups?

Abstract

We show that, in a weakly regular p-adic Lie group G, the subgroup ${\mathit{G}}_{\mathit{u}}$ 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 ${\mathit{G}}_{\mathit{u}}$