A note on fsg groups in p-adically closed fields

preprint2022arXivOpen access

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.

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