A generalization of a result on the sum of element orders of a finite group
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Marius Tărnăuceanu
Abstract
Let G be a finite group and let ψ(G) denote the sum of element orders of G. It is well-known that the maximum value of ψ on the set of groups of order n, where n is a positive integer, will occur at the cyclic group Cn. For nilpotent groups, we prove a natural generalization of this result, obtained by replacing the element orders of G with the element orders relative to a certain subgroup H of G.
Communicated by Miroslav Ploščica
Acknowledgement
The author is grateful to the reviewer for remarks which improve the previous version of the paper.
References
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Articles in the same Issue
- Regular papers
- Properties of implication in effect algebras
- On a nonlinear relation for computing the overpartition function
- Six-cycle systems
- Representation of bifinite domains by BF-closure spaces
- L-fuzzy cosets in universal algebras
- Density of sets with missing differences and applications
- Degree of independence of numbers
- A generalization of a result on the sum of element orders of a finite group
- A New fuzzy McShane integrability
- Hankel determinants of second and third order for the class 𝓢 of univalent functions
- Herglotz's theorem for Jacobi-Dunkl positive definite sequences
- Functional inequalities for Gaussian hypergeometric function and generalized elliptic integral of the first kind
- Existence on solutions of a class of casual differential equations on a time scale
- On a general system of difference equations defined by homogeneous functions
- Jordan amenability of banach algebras
- A new notion of orthogonality involving area and length
- Reeb flow invariant ∗-Ricci operators on trans-Sasakian three-manifolds
- A finite graph is homeomorphic to the Reeb graph of a Morse–Bott function
- On first countable quasitopological homotopy groups
