Counting subgroups of the groups ${\mathbb{Z}}_{n_1}\times \cdots \times {\mathbb{Z}}_{n_k}$: a survey

Abstract

We present a survey of exact and asymptotic formulas on the number of cyclic subgroups and total number of subgroups of the groups ${\mathbb{Z}}_{n_1}\times \cdots \times {\mathbb{Z}}_{n_k}$, where $k\ge 2$ and $n_1,\dots ,n_k$ are arbitrary positive integers.

book chapter. arXiv admin note: text overlap with arXiv:1611.03302

References in corpus (2)

• On the average number of subgroups of the group ${\mathbb{Z}}_m\times {\mathbb{Z}}_n$
• On the number of subgroups of a given exponent in a finite abelian group