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Every Abelian group is determined by a subgroup lattice. (English) Zbl 1156.20024

Summary: We prove that every Abelian group \(G\) is determined up to an isomorphism by the subgroup lattice of the group \(\mathbb{Z}\times G\) and some other similar results.

MSC:

20E15 Chains and lattices of subgroups, subnormal subgroups
20K27 Subgroups of abelian groups
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