A note on groups definable in the p-adic field
Logic
2018-07-25 v1 Group Theory
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.
Cite
@article{arxiv.1807.09079,
title = {A note on groups definable in the p-adic field},
author = {Anand Pillay and Ningyuan Yao},
journal= {arXiv preprint arXiv:1807.09079},
year = {2018}
}
Comments
7 pages