  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.
