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arXiv:1611.03302 [math.GR]AbstractReferencesReviewsResources

The number of subgroups of the group $\Bbb{Z}_m\times \Bbb{Z}_n \times \Bbb{Z}_r \times \Bbb{Z}_s$

László Tóth

Published 2016-11-10Version 1

We deduce direct formulas for the total number of subgroups and the number of subgroups of a given order of the group $\Bbb{Z}_m\times \Bbb{Z}_n \times \Bbb{Z}_r \times \Bbb{Z}_s$, where $m,n,r,s\in \Bbb{N}$. The proofs are by some simple group theoretical and number theoretical arguments based on Goursat's lemma for groups. Two conjectures are also formulated.

Comments: 13 pages, tables
Categories: math.GR, math.CO, math.NT
Subjects: 20K01, 20K27, 11A25, 11Y70
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