Subgroups of Finite Abelian Groups Having Rank Two via Goursat’s Lemma

Tóth, László

doi:10.2478/tmmp-2014-0021

Abstract

Using Goursat’s lemma for groups, a simple representation and the invariant factor decompositions of the subgroups of the group Z_m× Z_n are deduced, where m and n are arbitrary positive integers. As consequences, explicit formulas for the total number of subgroups, the number of subgroups with a given invariant factor decomposition, and the number of subgroups of a given order are obtained.

References

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Subgroups of Finite Abelian Groups Having Rank Two via Goursat’s Lemma

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