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Characterization of Finite Dedekind Groups

Published online by Cambridge University Press:  22 January 2016

Reinhold Baer
Reinhold Baer*
Affiliation:
Frankfurt University
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If U=U(0), U(i) is a maximal subgroup of U(i + 1) and U(n) = V, then we term the U(i) a densest chain connecting U and V; and n is the length of this chain. The subgroup U of V will furthermore be termed an n-uniserial subgroup of V if there exists one and only one densest chain connecting U and V and if its length is n. The principal aim of this note is to give characterizations of dedekind groups [ = groups all of whose subgroups are normal] in terms of the normality of uniserial subgroups. We quote one of our results:

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 1 , February 1966 , pp. 21 - 41
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Baer, Reinhold, Nilpotent groups and their generalisations, Trans. Amer. Math. Soc. 47, 393–434 (1940).CrossRefGoogle Scholar
[2] Fuchs, L., Abelian groups, Budapest (1958).Google Scholar
[3] Hall, Marshall Jr., The Theory of Groups, New York (1959).Google Scholar
[4] Kurosh, A. G., The Theory of Groups; 2nd english edition, New York (1960).Google Scholar
[5] Rédei, L., Die endlichen einstufig nicht nilpotenten Gruppen, Publications Math. Debrecen 4, 303–324 (1956).Google Scholar