English

A note on fsg groups in p-adically closed fields

Logic 2022-03-30 v2

Abstract

Let GG be a definable group in a pp-adically closed field MM. We show that GG has finitely satisfiable generics (fsg) if and only if GG is definably compact. The case M=QpM = \mathbb{Q}_p was previously proved by Onshuus and Pillay.

Keywords

Cite

@article{arxiv.2108.06092,
  title  = {A note on fsg groups in p-adically closed fields},
  author = {Will Johnson},
  journal= {arXiv preprint arXiv:2108.06092},
  year   = {2022}
}

Comments

10 pages; added acknowledgment and Remark 5.7, fixed typo

R2 v1 2026-06-24T05:05:16.384Z