Determinability of a Completely Decomposable Block-Rigid Torsion-Free Abelian Group by Its Automorphism Group

On Determinability of a Quotient Divisible Abelian Group of Rank 1 by Its Automorphism Group

“…Similar result was obtained for p = 3 [2]. Rank 1 torsion-free groups are not determined by their automorphism groups, but for direct sums of torsion-free groups of rank 1 (i.e., for completely decomposable torsion-free groups) necessary and sufficient conditions for determinability of a group by its automorphism group in some classes were found (see [3,4]). Among other things, the question of determinability of a group by its automorphism group was considered in the class of completely decomposable torsion-free groups whose direct summands of rank 1 have idempotent types [3].…”