Isomorphism of automorphism groups of mixed modules over a complete discrete valuation ring.
AuthorAdongo, Harun Paulo Kasera.
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PublisherThe University of Arizona.
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AbstractIsomorphisms of automorphism groups of reduced torsion abelian p-groups have recently been classified by W. Liebert [L1] and [L2] for p ≠ 2. The primary objective of this study is to investigate the isomorphisms of automorphism groups of reduced mixed modules M and N of torsion-free ranks < ∞ over a complete discrete valuation ring with totally projective torsion submodules t(M) and t(N) respectively. For modules over ℤ(p), p ≠ 2, we show that if AutM and AutN are isomorphic and the quotient modules M/t(M) and N /t(N) are divisible, then M ≃ N.