Resumen de P-localization of some classes of groups

Augusto Reynol Filho

• The aim for the present paper is to study the theory of P-localization of a group in a category C such that it contains the category of the nilpotent groups as a full sub-category. In the second section we present a number of results on P-localization of a group G, which is the semi-direct product of an abelian group A with a group X, in the category G of all groups. It turns out that the P-localized (GP) is completely described by the P-localized XP of X, A and the action w of X on A. In the third section, we present the construction of the theory of P-localization in the category of all groups which are extensions of nilpotent groups by finite abelian groups. Our proof follows rather closely the one presented in [2, chapter I], and is based on the classical interpretation of the second cohomology group of a group.