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Abelian groups whose subgroup lattice is the union of two intervals

Part of: Modular lattices, complemented lattices Abelian groups

Published online by Cambridge University Press:  09 April 2009

Simion Breaz  and
Grigore Călugăreanu
Simion Breaz
Affiliation:
Faculty of Mathematics, and InformaticsBabes-Bolyai University, Cluj-Napoca, Romania, e-mail: bodo@math.ubbcluj.ro
Grigore Călugăreanu
Affiliation:
Dept. Mathematics and Computer Sci, Faculty of Science, Kuwait University, State of Kuwait e-mail: calu@mcs. sci. kuniv.edu.kw
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Abstract

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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.

Keywords

subgroup latticeintervaltorsion abelian groupcocyclic groups

MSC classification

Secondary: 06C99: None of the above, but in this section 20K10: Torsion groups, primary groups and generalized primary groups 20K27: Subgroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 78 , Issue 1 , February 2005 , pp. 27 - 36
Copyright
Copyright © Australian Mathematical Society 2005

References

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