Armstrong, B.Brown, J.H.Clark, L.O.Courtney, K.Lin, Y.F.McCormick, K.Ramagge, J.2025-12-182025-12-182023Semigroup Forum, 2023; 107(3):609-6230037-19121432-2137https://hdl.handle.net/11541.2/36462In this note, we present criteria that are equivalent to a locally compact Hausdorff groupoid G being effective. One of these conditions is that G satisfies the C*-algebraic local bisection hypothesis; that is, that every normaliser in the reduced twisted groupoid C*-algebra is supported on an open bisection. The semigroup of normalisers plays a fundamental role in our proof, as does the semigroup of normalisers in cyclic group C*-algebras.enCopyright 2023 Springer. This article is licensed under a Creative Commons Attribution 4.0 International License. (http://creativecommons.org/licenses/by/4.0/)effective groupoidlocal bisection hypothesistwisted groupoid C*-algebraJournal article10.1007/s00233-023-10392-92-s2.0-85174309591