Upper bounds for the product of element orders of finite groups

Elena Di Domenico, Carmine Monetta, Marialaura Noce

Type: Article

Publication Date: 2023-03-29

Citations: 3

DOI: https://doi.org/10.1007/s10801-023-01222-w

Abstract

Abstract Let G be a finite group of order n , and denote by $$\rho (G)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ρ</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> the product of element orders of G . The aim of this work is to provide some upper bounds for $$\rho (G)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ρ</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> depending only on n and on its least prime divisor, when G belongs to some classes of non-cyclic groups.

Locations

Journal of Algebraic Combinatorics - View - PDF

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