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(2012)
Panorama of p-adicmodel theory
Samaria Montenegro, A. Onshuus, Pierre Simon (2016)
Stabilizers, groups with f-generics in NTP2 and PRC fieldsarXiv: Logic
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Groups definable in local and pseudofinite fields
A Onshuus, A Pillay (2008)
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L Belair (2012)
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E. Hrushovski, A. Pillay (2011)
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A. Onshuus, A. Pillay (2008)
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It is known Hrushovski and Pillay (Israel J Math 85:203–262, 1994) that a group G definable in the field $${\mathbb {Q}}_{p}$$ Q p of p-adic numbers is definably locally isomorphic to the group $$H({\mathbb {Q}}_{p})$$ H ( Q p ) of p-adic points of a (connected) algebraic group H over $${\mathbb {Q}}_{p}$$ Q p . We observe here that if H is commutative then G is commutative-by-finite. This shows in particular that any one-dimensional group G definable in $${\mathbb {Q}}_{p}$$ Q p is commutative-by-finite. This result extends to groups definable in p-adically closed fields. We prove our results in the more general context of geometric structures.
Archive for Mathematical Logic – Springer Journals
Published: Apr 29, 2019
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