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Abelian Groups with π-Regular Center of the Endomorphism Ring

The notion of π-regular endomorphism ring of an abelian group generalizing the notion of regular endomorphism ring was introduced by L. Fuchs and K.M. Rangaswamy. They described periodic abelian groups with π-regular endomorphism ring and found some necessary conditions for an abelian group to have π-regular endomorphism ring. In this paper, we study abelian groups with π-regular center of the endomorphism ring. We found necessary and sufficient conditions under which an abelian group has π-regular center of the endomorphism ring.