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arXiv · 1304.2961

On the subgroups of finite Abelian groups of rank three

Mario Hampejs·László Tóth
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Abstract

We describe the subgroups of the group $\Z_m \times \Z_n \times \Z_r$ and derive a simple formula for the total number $s(m,n,r)$ of the subgroups, where $m,n,r$ are arbitrary positive integers. An asymptotic formula for the function $n\mapsto s(n,n,n)$ is also deduced.

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Mario Hampejs, László Tóth. 2013-04-10. On the subgroups of finite Abelian groups of rank three. https://arxiv.org/abs/1304.2961

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