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

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

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.

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Veröffentlicht in:Bulletin of the Australian Mathematical Society 2020-04, Vol.101 (2), p.201-206
1. Verfasser: TĂRNĂUCEANU, MARIUS
Format: Artikel
Sprache:eng
Schlagworte:
Automorphisms
Group theory
Orbits
Subgroups
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Beschreibung
Zusammenfassung: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.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972719000601