CONTENTS § 1. Introduction.......................................................................................................................................... 5 § 2. Definitions and lemmas................................................................................................................... 7 § 3. Theorem on the isomorphism of subdirect sums with the same kernels............................. 15 § 4. The group of automorphisms of a torsion-free abelian group of rank two............................. 53 § 5. The ring of endomorphisms of torsion-free abelian group of rank two................................... 63 References.................................................................................................................................................. 73