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.
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
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