On the number of cyclic subgroups of a finite abelian group

Details On the number of cyclic subgroups of a finite abelian group On the number of cyclic subgroups of a finite abelian group

2012-03-28

arxiv.org/abs/1203.6201v1

Mathematics

Group Theory

8 pages

Scientific paper

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. The average order of the function $n\mapsto c^{(r)}(n)$, representing the number of cyclic subgroups of the direct factor of $r$ copies of the cyclic group of order $n$ is also considered.

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