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The relationship between the endomorphism ring and the automorphism group of an abelian p-group has been extensively investigated. It is known that theautomorphism group need not generate the full endomorphism ring. In this paper we investigate the analagous problem for torsion free modules over a complete discrete valuation ring obtaining similar results.
Goldsmith, Brendan:On endomorphism and automorphisms of some torsion-free modules. In Abelian Group Theory ed. by R. Gobel and E.A. Walker, Gordon and Breach, N.Y., 1987, pp.417-423. doi.org/10.21427/dt5s-hx29