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THE NUMBER OF CYCLIC SUBGROUPS OF FINITE ABELIAN GROUPS AND MENON’S IDENTITY

Published online by Cambridge University Press:  17 May 2019

MARIUS TĂRNĂUCEANU*
Affiliation:
Faculty of Mathematics, “Al.I. Cuza” University, Iaşi, Romania email [email protected]

Abstract

We give a new formula for the number of cyclic subgroups of a finite abelian group. This is based on Burnside’s lemma applied to the action of the power automorphism group. The resulting formula generalises Menon’s identity.

Type
Research Article
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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