Subgroups of finite Abelian groups having rank two via Goursat’s lemma
Tóth, László
Tatra Mountains Mathematical Publications, Tome 58 (2014), / Harvested from Mathematical Institute
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Using Goursat’s lemma for groups, a simple representation and the invariant factor decompositionsof the subgroups of the group $\mathbb{Z}_m \times  \mathbb{Z}_n$ are deduced, where $m$ and $n$ are arbitrarypositive integers. As consequences, explicit formulas for the total number of subgroups,the number of subgroups with a given invariant factor decomposition, and the number ofsubgroups of a given order are obtained.

Publié le : 2014-01-01
DOI : https://doi.org/10.2478/tatra.v59i0.335 
@article{335,
     title = {Subgroups of finite Abelian groups having rank two via Goursat's lemma},
     journal = {Tatra Mountains Mathematical Publications},
     volume = {58},
     year = {2014},
     doi = {10.2478/tatra.v59i0.335},
     language = {EN},
     url = {http://dml.mathdoc.fr/item/335}
}

Tóth, László. Subgroups of finite Abelian groups having rank two via Goursat’s lemma. Tatra Mountains Mathematical Publications, Tome 58 (2014) . doi : 10.2478/tatra.v59i0.335. http://gdmltest.u-ga.fr/item/335/