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Abelian groups whose subgroup lattice is the union of two intervals. (English) Zbl 1080.20023
The authors show that the groups defined in the title of their paper are precisely the Abelian torsion groups having a primary component of the form \(A\times B\) where \(A\simeq C_{p^n}\) (\(p\in\mathbb{P}\), \(n\in\mathbb{N}\cup\{\infty\}\)) and \(\exp B<\exp A\).

MSC:
20E15 Chains and lattices of subgroups, subnormal subgroups
20K10 Torsion groups, primary groups and generalized primary groups
20K27 Subgroups of abelian groups
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References:
[1] DOI: 10.1090/S0002-9904-1946-08602-4 · Zbl 0060.06505
[2] DOI: 10.1016/0021-8693(89)90171-3 · Zbl 0679.20024
[3] Călugăreanu, Proceedings of Groups St Andrews 2001 in Oxford pp 59– (2003)
[4] Fuchs, Infinite abelian groups 1 (1970)
[5] Schmidt, Subgroup lattices of groups 14 (1994) · Zbl 0843.20003
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