Subgroups of finite abelian groups having rank two via Goursat's lemma

Year, pages: 2014, 93 - 103

Using Goursat's lemma for groups, a simple representation and the invariant factor decompositions of the subgroups of the group $\Z_m × \Z_n$ are deduced, where $m$ and $n$ are arbitrary positive integers. As consequences, explicit formulas for the total number of subgroups, the number of subgroups with a given invariant factor decomposition, and the number of subgroups of a given order are obtained.

Tóth, L. 2014. Subgroups of finite abelian groups having rank two via Goursat's lemma. In Tatra Mountains Mathematical Publications, vol. 59, no.2, pp. 93-103. 1210-3195.

Tóth, L. (2014). Subgroups of finite abelian groups having rank two via Goursat's lemma. Tatra Mountains Mathematical Publications, 59(2), 93-103. 1210-3195.