Harmonic numbers and finite groups.

DOI10.4171/RSMUP/132-3zbMath1314.20020OpenAlexW1985267466MaRDI QIDQ481022

Ashish Kumar Das, Sekhar Jyoti Baishya

Publication date: 12 December 2014

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/rsmup/132-3

zbMATH Keywords

finite groupsharmonic numbersorders of normal subgroupsharmonic groupsnumbers of normal subgroupssums of orders

Mathematics Subject Classification ID

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

Related Items

On a group-theoretical generalization of the Gauss formula

Uses Software

• GAP
• MathOverflow

Cites Work

• Über das harmonische Mittel der Teiler einer natürlichen Zahl. I, II
• All harmonic numbers less than \(10^{14}\)
• The primitive soluble permutation groups of degree less than 256
• The theory of finite groups. An introduction.
• Finite groups determined by an inequality of the orders of their subgroups.
• Numbers whose positive divisors have small integral harmonic mean
• On Arithmetic Functions of Finite Groups
• All numbers whose positive divisors have integral harmonic mean up to $\mathbf {300}$
• On the Averages of the Divisors of a Number
• On Numbers with Integral Harmonic Mean