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ON NON-COMPACT p-ADIC DEFINABLE GROUPS

Part of: Model theory

Published online by Cambridge University Press:  22 November 2021

WILL JOHNSON Open the ORCID record for WILL JOHNSON [Opens in a new window]  and
NINGYUAN YAO Open the ORCID record for NINGYUAN YAO [Opens in a new window]
WILL JOHNSON
Affiliation:
SCHOOL OF PHILOSOPHY FUDAN UNIVERSITY 220 HANDAN ROAD, GUANGHUA WEST BUILDING, ROOM 2503 SHANGHAI 20043, CHINAE-mail:willjohnson@fudan.edu.cnE-mail:yaony@fudan.edu.cn
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Abstract

In [16], Peterzil and Steinhorn proved that if a group G definable in an o-minimal structure is not definably compact, then G contains a definable torsion-free subgroup of dimension 1. We prove here a p-adic analogue of the Peterzil–Steinhorn theorem, in the special case of abelian groups. Let G be an abelian group definable in a p-adically closed field M. If G is not definably compact then there is a definable subgroup H of dimension 1 which is not definably compact. In a future paper we will generalize this to non-abelian G.

Keywords

definable groupsNIP groupsp-adic numbers

MSC classification

Primary: 03C60: Model-theoretic algebra 03C98: Applications of model theory
Type
Article
Information
The Journal of Symbolic Logic , Volume 87 , Issue 1 , March 2022 , pp. 188 - 213
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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