MATH 422 Introduction to Abelian Groups

Abelian groups. Quotient groups. Isomorphism theorems. Torsion part of the group. Decomposition of torsion groups into direct sum of primary groups. Divisibility. Injective groups. Structure of divisible groups. Projective groups. Free groups. Existence of epimorphisms from a projective groups and of monomorphisms into injective groups. Pure subgroups. Basic subgoups. Bounded pure subgroups. Classification of torsion-free groups of rank one.