On the number of subgroups of the group ${\mathbb{Z}}_{m_1}\times {\mathbb{Z}}_{m_2}$ with $m_1{m}_2\le x$ such that $m_1{m}_2$ is a $k$-th power

Yankun Sui, Dan Liu, Boling Zhou

Let ${\mathbb{Z}}_m$ be the additive group of residue classes modulo $m$ and $s(m_1,m_2)$ denote the number of subgroups of the group ${\mathbb{Z}}_{m_1}\times {\mathbb{Z}}_{m_2}$, w…