2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171104We construct examples of localizations in the category of groups which take the Mathieu group $M_{11}$ to groups of arbitrarily large cardinality which are ``abelian up to finitely many generators''. The paper is part of a broader study on the group theoretic properties which are or are not preserved by localizations.15 pages, to appear in J. AlgebraGroup Theory20J15; 20D99text