Weak regularity and one-parameter subgroups of definable p-adic Lie groups

2026/07/26 by Zhentao Zhang
#math.LO

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Abstract

We prove that every group G definable in the pure p-adic field ℚ_p is weakly regular. We show that every one-parameter subgroup is definable. We also show that its one-parameter core G_u, together with a suitable regular open subgroup G_Ω, is definable. Finally, we show that if H is a dfg component of G, then G_u=⟨(H^g)_u:g∈ G⟩. In fact, G_u is a finite product of the one-parameter cores of finitely many conjugates of H. In particular, when G is definably amenable, G_u=H_u.

Citations

• One-dimensional subgroups and connected components in non-abelian p-adic definable groups
• How far are p-adic Lie groups from algebraic groups?

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• One-dimensional subgroups and connected components in non-abelian p-adic definable groups
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