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arXiv:1304.2961 [math.GR]AbstractReferencesReviewsResources

On the subgroups of finite Abelian groups of rank three

Mario Hampejs, László Tóth

Published 2013-04-10Version 1

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.

Comments: 11 pages, 3 tables
Journal: Annales Univ. Sci. Budapest., Sect. Comp. 39 (2013), 111-124
Categories: math.GR, math.NT
Subjects: 20K01, 20K27, 11A25, 11N37
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