Abelian groups whose subgroup lattice is the union of two intervals

Abelian groups whose subgroup lattice is the union of two intervals

In this note we characterize the abelian groups G which have two different proper subgroups N and M such that the subgroup lattice L(G)=[0, M]∪ [N, G] is the union of these intervals.

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Bibliographische Detailangaben
Veröffentlicht in:Journal of the Australian Mathematical Society (2001) 2005-02, Vol.78 (1), p.27-36
Hauptverfasser: Breaz, Simion, Călugăreanu, Grigore
Format: Artikel
Sprache:eng
Schlagworte:
20K10
20K27
cocyclic groups
Group theory
interval
Intervals
Lattices (mathematics)
primary 06C99
subgroup lattice
Subgroups
torsion abelian group
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Beschreibung
Zusammenfassung:In this note we characterize the abelian groups G which have two different proper subgroups N and M such that the subgroup lattice L(G)=[0, M]∪ [N, G] is the union of these intervals.
ISSN:1446-7887
1446-8107
DOI:10.1017/S1446788700015548