Primary Abelian Groups Whose Countable Subgroups Have Countable Closure

Abstract

Two subgroups H and K of G are said to be equivalent if there is an automorphism of G that maps H onto K. Using Martin’s Axiom, we establish an equivalence theorem for countable subgroups of a class of groups called c.c. groups. More precisely, we find necessary and sufficient conditions for two countable subgroups of a c.c. group to be equivalent. A p-primary abelian group G is a c.c. group if every countable subgroup has countable closure in the p-adic topology. The equivalence theorem is then used to obtain some structural results and homological properties of c.c. groups.

Supported by NSF Grant DMS 92-03199