A NEW MENON-TYPE IDENTITY DERIVED FROM GROUP ACTIONS

MARIUS TĂRNĂUCEANU

Faculty of Mathematics, “Al.I. Cuza” University of Iași, Iași, ROMANIA e-mail: tarnauc@uaic.ro

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 group. It is based on applying the weighted form of Burnside’s lemma to a natural group action.

Keywords

Menon’s identity weighted Burnside’s lemma group action sum of element orders sum of cyclic subgroup orders
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