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By R. Göbel, C. Metelli, A. Orsatti, L. Salce

ISBN-10: 3211818472

ISBN-13: 9783211818473

ISBN-10: 3709128145

ISBN-13: 9783709128145

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Additional resources for Abelian Groups and Modules: Proceedings of the Udine Conference Udine April 9–14, 1984

Sample text

3 says can be mapped D 2 p -bounded finite valuated Theorem 4). We extend this 2 result to p -bounded valuated groups with finitely many values. 1. G(lol sum of x E A p-valuated group with a finite value. 2 p -Bounded Valuated Groups. is a is a p. 7 says that group Conversely, it suffices to get a nonzero then to any element in Let C p-valuated groups with finite value sets. from ~ set is 0. 6, any direct product of copies of direct sum of copies of c FC(A) + n) If 0 G is a nonzero valuated group such that n < for some w, then G has a 2 p G "' 0 nonzero cyclic summand.

Non-isomorphic structures as We applied this in [Sh 3] for separable The author would like to thank the United States Israel Science Foundation for partially supporting this research. Binational S. Shelah 38 p-groups illustrating the impossibility of a groups by reasonable invariants. algebra in every details. 6. been such [Sh 7] for more results and [Sh 1] , We will continue with the combinatorics of [ Sh 4], utilized GBbel and Shelah in [GS ]. Dugas and GBbel in [DG 1], [DG 2] and by by The nicest feature of these fact that they were carried out in ZFC.

Then v(a + k) and so We shall show that the sum and 1, ~ a • a 2 + pa' a 2 + h,. ,.. 3 we can find 0. va • htA(a) va > htA(a),. 0 If b If a E A If = O, ~ so is possible, whence 4 would have value Similarly no element of in 8 p 2 had value sequence sequence B = 0. If X in can (1,2,3), would be a summand of B(l) Thus B B. had 30 R. Hunter- F. Richman- E. Walker value sequence would be a (0,2,3), then B. summand of p 2 B(0,2) • 0. Therefore 2 B(4) + p B(l) .. 0, F(B) • Hence no such p~(0,2) F(B) • 8(4) + is X a so possible, 0, whence so the lemma says that any direct sum of copies of the simply presented valuated group of type (0-1,2)-3 in 8 is a summand of B.

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Abelian Groups and Modules: Proceedings of the Udine Conference Udine April 9–14, 1984 by R. Göbel, C. Metelli, A. Orsatti, L. Salce


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