On K-large and generalized K-large Abelian groups

The concepts of K-large and generalized K-large Abelian groups are introduced, and their main properties and interconnections are studied. We consider groups that are K-large (generalized K-large) with respect to the class of all groups and torsion-free groups. The main focus is on the case where K consists of bounded p-groups for an infinite set of prime numbers p. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 3, pp. 51–60, 2007.