# zbMATH — the first resource for mathematics

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
##### Keywords:
subgroup lattices; intervals; Abelian torsion groups
Full Text:
##### 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.