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• W3102094349 startingPage "1037" @default.
• W3102094349 abstract "We consider profinite groups as 2-sorted first order structures, with a group sort, and a second sort which acts as an index set for a uniformly definable basis of neighbourhoods of the identity. It is shown that if the basis consists of {em 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 which 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." @default.
• W3102094349 created "2020-11-23" @default.
• W3102094349 creator A5033212640 @default.
• W3102094349 creator A5065008031 @default.
• W3102094349 date "2016-10-19" @default.
• W3102094349 modified "2023-09-27" @default.
• W3102094349 title "Profinite groups with NIP theory andp-adic analytic groups" @default.
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• W3102094349 doi "https://doi.org/10.1112/blms/bdw064" @default.
• W3102094349 hasPublicationYear "2016" @default.
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