Read e-book online Abelian Groups and Modules: Proceedings of the Udine PDF

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

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Definition: E a GJ , and for some { ,g gf the class ~~).

4) Let J~ be the family of (f,N) such that fl, 1U <~ f N I" L(N ) = '\'1 for and let (f'l'l,N'I'l) be as above (it is easy to show that .. I, •. l} L(N) = U L(N ) N =UN~ U {(f1 ,N1 ) some 'l'l v. I' L(N )) • 'l'l (f't\,N'I'l) is uniquely determined, -notice d), e) in 2)). 6) Let J~ = {(f'l'l,N'I'l): for some (f1 ,N1 ) (l(n), {(f 1 ,N 1 ):l~n}6J'\1 }, and we adopt the conventions of 4). 7) Usually we identify Ji and Ji (for i~~). ), 'tl" n is just such ~Rang(f). 4. ), ~ (B l (CIL) E cf >. non-decreasing.

25 Subgroups of Bounded Abelian Groups PROOF. 5), map from to Thus we can map x COROLLARY 2. 8. direct sum of map PROOF. C. If vx a a, C such that C(a) C of order A to a direct sum of copies of As every subroup of a p-nice, the subgroup 3. direct FC(A) cyclics is 0. As ~ A(a) 0. ~ p-group, and C a A Then there is a such that = Ker FC(A) is nice in c. Every [HRWl; A. 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.

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