Representing and counting the subgroups of the group Z_m x Z_n

Mario Hampejs; Nicki Holighaus; László Tóth; Christoph Wiesmeyr

Representing and counting the subgroups of the group Z_m x Z_n

Group Theory 2014-10-28 v3 Combinatorics Number Theory

Authors: Mario Hampejs , Nicki Holighaus , László Tóth , Christoph Wiesmeyr

Abstract

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.

Keywords

subgroups finite abelian groups invariant factor decomposition group representation counting formulas direct product of cyclic groups

Cite

@article{arxiv.1211.1797,
  title  = {Representing and counting the subgroups of the group Z_m x Z_n},
  author = {Mario Hampejs and Nicki Holighaus and László Tóth and Christoph Wiesmeyr},
  journal= {arXiv preprint arXiv:1211.1797},
  year   = {2014}
}

Comments

12 pages, 1 figure, revised

Representing and counting the subgroups of the group Z_m x Z_n

Abstract

Keywords

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