Representing and counting the subgroups of the group Z_m x Z_n

Abstract

We deduce a simple representation and the invariant factor decompositions of the subgroups of the group ${\mathbb{Z}}_m\times {\mathbb{Z}}_n$, where $m$ and $n$ are arbitrary positive integers. We obtain formulas for the total number of subgroups and the number of subgroups of a given order.

12 pages, 1 figure, revised

References in corpus (2)

• Menon's identity and arithmetical sums representing functions of several variables
• On the number of cyclic subgroups of a finite abelian group

Cited by in corpus (3)

• Efficient algorithms for discrete Gabor transforms on a nonseparable lattice
• Cyclicity degrees of finite groups
• An Arithmetic Function Arising from the Dedekind $\psi$ Function