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ENDOMORPHISM RINGS OF ABELIAN GROUPS WITH AMPLE DIVISIBLE SUBGROUPS WARREN MAY Let G and G* be abelian groups whose endomorphism rings E(G) and E(G*) are isomorphic. There are few theorems in the literature giving circumstances under which isomorphism of G with G* can be inferred. If we are dealing with torsion groups, then the well-known theorem of Baer and Kaplansky [3; Theorem 28] applies. Hauptfleisch [2] and Wolfson [7, 8] have obtained results for certain classes of torsion- free groups. The case of mixed abelian groups of torsion-free rank one has been considered by May and Toubassi [4, 5]. All of these results place conditions on both G and G*. There are fewer theorems that place restrictions only on G. As an example, the torsion groups G for which one can conclude that G is isomorphic to G* are determined in [6]. In this paper, we shall give a class of abelian groups such that if G is in the class, then isomorphism of E(G) with £(G*) implies isomorphism of G with G*. In studying the isomorphism problem, it is apparent that an abundance of available mappings increases the probability of obtaining positive results. Consequently, we wish to consider
Bulletin of the London Mathematical Society – Wiley
Published: Nov 1, 1978
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