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A lattice characterization of the lattice of subgroups of an Abelian group containing two independent aperiodic elements. (Italian) Zbl 0595.20025
An element, x, of a lattice L is cyclic if x/0 is distributive and satisfies the maximal condition, and x is torsion-free if x/0 is free of atoms. The author defines L to be a G-lattice if it satisfies conditions Cl-C8 (which are too detailed to give here). He continues work from an earlier paper by proving that L is isomorphic with the lattice of subgroups of an abelian group which contains two independent aperiodic elements if and only if L is a G-lattice which contains nonzero cyclic torsion-free elements x and y such that $$x\wedge y=0$$.
Reviewer: W.E.Deskins
##### MSC:
 20E15 Chains and lattices of subgroups, subnormal subgroups 20K27 Subgroups of abelian groups 06B15 Representation theory of lattices
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##### References:
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