English

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.

Keywords

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

R2 v1 2026-06-23T03:12:24.762Z