Some number-theoretic identities from group actions.

DOI10.1007/s12215-009-0010-6zbMath1187.20015OpenAlexW2059655213MaRDI QIDQ1032595

Balasubramanian Sury

Publication date: 26 October 2009

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12215-009-0010-6

zbMATH Keywords

Cauchy-Frobenius formulageneralized totient functiongraph actionslinear actions of finite linear groupsnot-Burnside lemma

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Arithmetic functions; related numbers; inversion formulas (11A25) General theory for finite permutation groups (20B05)

Related Items (22)

A Menon-type identity in residually finite Dedekind domains ⋮ Menon-type identities derived from actions of subgroups of general linear groups ⋮ A generalization of Arai-Carlitz's identity ⋮ A Menon-type identity using Klee's function ⋮ Unnamed Item ⋮ A Menon-type identity with multiplicative and additive characters ⋮ Another generalization of Menon’s identity ⋮ Proofs, generalizations and analogs of Menon's identity: a survey ⋮ On a question of Sury ⋮ Another generalization of Menon’s identity in the ring of algebraic integers ⋮ A generalization of Menon's identity ⋮ A NEW MENON’S IDENTITY FROM GROUP ACTIONS ⋮ Another regular Menon-type identity in residually finite Dedekind domains ⋮ IDEAL CHAINS IN RESIDUALLY FINITE DEDEKIND DOMAINS ⋮ A Menon-type identity with many tuples of group of units in residually finite Dedekind domains ⋮ Menon-type identities with additive characters ⋮ A generalization of Menon’s identity with Dirichlet characters ⋮ Menon-type identities with respect to sets of units ⋮ A Menon-type identity concerning Dirichlet characters and a generalization of the gcd function ⋮ THE NUMBER OF CYCLIC SUBGROUPS OF FINITE ABELIAN GROUPS AND MENON’S IDENTITY ⋮ On a generalization of Menon-Sury identity to number fields involving a Dirichlet character ⋮ A Menon-type identity with Dirichlet characters in residually finite Dedekind domains

Cites Work

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