Submission date: 24 July 2018

Abstract:

It is known that a group G definable in the field of p-adic numbers is definably locally isomorphic to the group of Q_p-points of a connected algebraic group H defined over Q_p. We show that if H is commutative then G is commutative-by-finite. It follows in particular that any one-dimensional group definable in Q_p is commutative-by-finite. The results extend to groups definable in p-adically closed fields.

Mathematics Subject Classification: 03C60, 20G25, 22E35

Keywords and phrases:

Full text arXiv 1807.09079: pdf, ps.