A note on groups definable in the p-adic field

2018/07/24 by Pillay, Anand, Yao, Ningyuan
#03C60 #20G25 #22E35 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · doi:10.48550/arxiv.1807.09079

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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