On the number of cyclic subgroups of a finite abelian group

Abstract

We prove by using simple number-theoretic arguments formulae concerning the number of elements of a fixed order and the number of cyclic subgroups of a direct product of several finite cyclic groups. We point out that certain multiplicative properties of related counting functions for finite Abelian groups are immediate consequences of these formulae.

6 pages, revised, short form

Cited by in corpus (4)

• Cyclicity degrees of finite groups
• Groups having 12 cyclic subgroups
• Some thoughts on pseudoprimes
• Modular tensor categories, subcategories, and Galois orbits