A note on fsg $\text{fsg}$ groups in p-adically closed fields

Pub Date : 2023-05-24 DOI:10.1002/malq.202200026
Will Johnson
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Abstract

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

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p极闭域中fsg$\text{fsg}$群的一个注记
设G是p-自由闭域M中的可定义群。我们证明了G具有有限可满足泛型(fsg$\text{fsg}$)当且仅当G是可定义紧致的。案例M=Q p$M=\mathbb{Q}_pOnshuus和Pillay之前已经证明了$。
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