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

DOI10.1017/S0004972719000601zbMath1444.11016arXiv1811.04563OpenAlexW2949157432WikidataQ127866967 ScholiaQ127866967MaRDI QIDQ5222135

Marius Tărnăuceanu

Publication date: 1 April 2020

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.04563

zbMATH Keywords

Cauchy-Frobenius-Burnside lemmaMenon identitypower automorphism group

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Arithmetic functions; related numbers; inversion formulas (11A25)

Related Items (1)

Proofs, generalizations and analogs of Menon's identity: a survey

Cites Work

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• Introduction to arithmetical functions
• On certain trigonometric sums in several variables
• Subgroup lattices of groups
• Menon-type identities derived from actions of subgroups of general linear groups
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• Menon's identity in residually finite Dedekind domains
• An arithmetic method of counting the subgroups of a finite abelian group
• Menon's identity and arithmetical sums representing functions of several variables
• Arithmetical sums in regular convolutions.
• Another generalization of Menon’s identity
• Menon-type identities concerning Dirichlet characters
• On the number of cyclic subgroups of a finite abelian group

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