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Abelian Group Theory: Proceedings of the 2nd New Mexico - download pdf or read online

By Robert B. Warfield Jr. (auth.), David M. Arnold, Roger H. Hunter, Elbert A. Walker (eds.)

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Additional resources for Abelian Group Theory: Proceedings of the 2nd New Mexico State University Conference, Held at Las Cruces, New Mexico, December 9–12, 1976

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Let S and S' be two collections of height matrices, S ~ b S' , with respect to a group A. Then and suppose If B is any group with a decomposition basis X such that H(X) "~S, then there is a decomposition basis Y of B such that H(Y) KS'. Aside from ensuring that the concept of basis-equivalence is independent of a particular group, Lemma 4 also guarantees that basis-equivalence lence relation. is an equiva- Given any height matrix M, there is a rank one group A with an element x E A of infinite order such that H(x) = M.

38. A. E. Stratton, Mixed modules ring, Proc. London Math. Soc. 39. A. E. Stratton, A splitting theorem for mixed Abelian groups, Proc. Conf. on Abelian Groups (November, 1972), Symposia Mathematica 13,' Acadmemic Press,'London, 1974, pp. 109-125. 40. C. Walker and R. B. , Unique decomposition and isomorphic refinement theorems in an additive category, J. Pure and AppI. AI~. 7 (1976), 347-359. 41. E. A. Walker, Ulm's theorem for totally projective Amer. Math. Soc. 37 (1973), 387-392. 42. K. Alg.

It is again easy to see that a simply p r e s e n t e d group is a direct sum of groups of rank one. It is also easy to see that a group of rank one is a summand of a simply p r e s e n t e d group if and only if its localizations condition, so the rank one groups w h i c h appear are p r e c i s e l y those con- sidered in T h e o r e m i. M = 8ieI Mi' class e where One w o u l d next each Mi of Ulm matrices, such that U(M i) = e. invariants of the group to ignore to let g(e,M) Unfortunately, M, T h e o r e m 13.

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