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arXiv · 1807.09079

A note on groups definable in the p-adic field

Anand Pillay·Ningyuan Yao
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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.

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Anand Pillay, Ningyuan Yao. 2018-07-24. A note on groups definable in the p-adic field. https://arxiv.org/abs/1807.09079

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