Orbits of tuples and subgroups in abelian groups
Institute of Mathematical Sciences, Chennai.
A tuple (or subgroup) in a group is said to degenerate to another if the latter is an endomorphic image of the former. In a countable reduced abelian group, it is shown that if tuples (or finite subgroups) degenerate to each other, then they lie in the same automorphism orbit. The proof is based on techniques that were developed by Kaplansky and Mackey in order to give an elegant proof of Ulm's theorem.