The number of cyclic subgroups of finite abelian groups and Menon's identity

Marius T\u{a}rn\u{a}uceanu

The number of cyclic subgroups of finite abelian groups and Menon's identity

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arxiv 1811.04563 v1 pith:LVUT62H6 submitted 2018-11-12 math.GR

Marius Tărnăuceanu This is my paper · ORCID

classification math.GR

keywords abeliancyclicfinitegroupidentitymenonnumbersubgroups

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In this note, we give a new formula for the number of cyclic subgroups of a finite abelian group. This is based on applying the Burnside's lemma to a certain group action. Also, it generalizes the well-known Menon's identity.

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