## Abelian Group Theory: Proceedings of the Conference held at the University of Hawaii, Honolulu, USA, December 28, 1982 - January 4, 1983 |

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algebra assume basic subgroup basic submodules Butler group cardinality closed submodules commutative completely decomposable group contains Corollary coset coset condition countable cyclic groups decomposition Dedekind defined definition denote direct sum direct summand divisible elements endomorphism rings epimorphism equivalent exact sequence exists Ext(B finite rank follows Fuchs functor Galois group G group of finite Hence Hom(B homomorphism I-split ideal idempotent implies induces Infinite Abelian Groups integer isomorphic Lemma Let G m-separable Math matrix maximal modules monomorphism morphism non-zero p-adic p-group p-map p-rank preradical prime proj.dim projective dimension Proof Proposition prove pure exact pure injective pure subgroup pure submodule quasi-isomorphic quotient R-module reduced result satisfies separable p-group socle splitting strongly indecomposable subgroup of G subring subset sum of cyclic Suppose Theorem topology torsion-free abelian group torsion-free group torsion-free R-module type graph Ulm invariants valuated group valuation domain