Communications in algebra vol:31 issue:1 pages:389-402
Any localization functor on the category Grp of groups gives rise to a radical and an idempotent radical (possibly coinciding) which determine an epireflection, respectively a reduction. We describe how the classes of local groups for this epireflection and reduction can be obtained by application of standard closure operations on the class of local groups for the original localization. We furthermore characterize the class of acyclic groups for a given localization as a certain closed complement of its local groups. This approach through closure operations allows us to associate with any orthogonal pair on Grp, not necessarily reflective, an epireflection and a reduction which are in some sense maximal.