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