Representing and counting the subgroups of the group Z_m x Z_n

Christoph Wiesmeyr; L\'aszl\'o T\'oth; Mario Hampejs; Nicki Holighaus

arxiv: 1211.1797 · v3 · pith:KTGQ3ZYNnew · submitted 2012-11-08 · 🧮 math.GR · math.CO· math.NT

Representing and counting the subgroups of the group Z_m x Z_n

Mario Hampejs , Nicki Holighaus , L\'aszl\'o T\'oth , Christoph Wiesmeyr This is my paper

classification 🧮 math.GR math.COmath.NT

keywords subgroupsgroupnumberarbitrarycountingdecompositionsdeducefactor

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We deduce a simple representation and the invariant factor decompositions of the subgroups of the group $\Bbb{Z}_m \times \Bbb{Z}_n$, 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.

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