Abstract
Rotman [11;Corollary B] proved 1963 a certain analogon of the theorem of Jordan-Hölder for torsion-free abelian groups of finite rank defining composition sequences to be chains of pure subgroups of maximal length. For groups of rank 2 Beaumont and Pierce [2] got the complete analogon of Jordan-Hölder. It will be shown here that two composition sequences in torsion-free groups and Dedekind modules of finite rank have the same sum-type,i.e. the sum of types of composition factors. This is the complete transfer of the theorem of Jordan-Hölder.
Keywords
- Type Sequence
- Direct Summand
- Composition Sequence
- Finite Rank
- Composition Factor
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Research supported by grant Mu 628/1–1 from the Deutsche Forschungsgemeinschaft
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© 1983 Springer-Verlag Berlin Heidelberg
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Mutzbauer, O. (1983). Type Graph. In: Göbel, R., Lady, L., Mader, A. (eds) Abelian Group Theory. Lecture Notes in Mathematics, vol 1006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21560-9_10
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DOI: https://doi.org/10.1007/978-3-662-21560-9_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12335-4
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