Localization and Genus in Group Theory

Abstract

Abstract. We provide a unifying category theoretical framework to discuss various kinds of local global phenomena. Specializing to localization of groups at sets of primes P , we identify a large class of groups for which localization supports a passage from local information to global information. Local global principles for groups in this class are established and used to calculate certain homomorphism sets as well as splittings of epimorphisms and monomorphisms from local data.

Induced Morphisms Between Localization Genera of Groups

“…Aspects of localization as in groups and related categories have been studied in a unified way in a categorical setting (see [8] for instance). In this paper, our presentation is rather more specific to groups.…”