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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
Abstract 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 .