Pillay's conjecture for groups definable in weakly o‐minimal non‐valuational structures | Zendy

Eleftheriou Pantelis E. | Zendy

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Pillay's conjecture for groups definable in weakly o‐minimal non‐valuational structures

Author(s) -

Eleftheriou Pantelis E.

Publication year - 2021

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms.12494

Subject(s) - mathematics , conjecture , finitely generated abelian group , extension (predicate logic) , group (periodic table) , combinatorics , pure mathematics , topology (electrical circuits) , discrete mathematics , physics , computer science , quantum mechanics , programming language

Let G be a group definable in a weakly o‐minimal non‐valuational structure M . Then G / G 00 , equipped with the logic topology, is a compact Lie group, and if G has finitely satisfiable generics, then dim ( G / G 00 ) = dim ( G ) . Our main technical result is that G is a dense subgroup of a group definable in the canonical o‐minimal extension of M .

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