Macpherson, HD orcid.org/0000-0003-0277-7561 and Tent, K (2016) Profinite groups with NIP theory and p-adic analytic groups. Bulletin of the London Mathematical Society, 48 (6). pp. 1037-1049. ISSN 0024-6093
Abstract
We consider profinite groups as 2‐sorted first‐order structures, with a group sort, and a second sort that acts as an index set for a uniformly definable basis of neighbourhoods of the identity. It is shown that if the basis consists of all open subgroups, then the first‐order theory of such a structure is NIP (that is, does not have the independence property) precisely if the group has a normal subgroup of finite index that is a direct product of finitely many compact p ‐adic analytic groups, for distinct primes p . In fact, the condition NIP can here be weakened to NTP 2 . We also show that any NIP profinite group, presented as a 2‐sorted structure, has an open prosoluble normal subgroup.
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Copyright, Publisher and Additional Information: | (c) 2016, London Mathematical Society. This is an author produced version of a paper accepted for publication in Bulletin of the London Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy. | ||||
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Institution: | The University of Leeds | ||||
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) | ||||
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Depositing User: | Symplectic Publications | ||||
Date Deposited: | 09 Aug 2016 13:23 | ||||
Last Modified: | 10 May 2019 10:56 | ||||
Published Version: | http://dx.doi.org/10.1112/blms/bdw064 | ||||
Status: | Published | ||||
Publisher: | London Mathematical Society | ||||
Identification Number: | https://doi.org/10.1112/blms/bdw064 |