Abstract
In this short note, we give a new Menon-type identity involving the sum of element or-ders and the sum of cyclic subgroup orders of a finite abelian group. This is based on the weighted form of Burnside’s lemma applied to the action of the power automorphism group.
Cuvinte cheie
Menon’s identity
weighted Burnside’s lemma
group action
sum of element orders
sum of cyclic subgroup orders
abelian group