ON GROUPS WITH AVERAGE ELEMENT ORDERS EQUAL TO THE AVERAGE ELEMENT ORDER OF THE ALTERNATING GROUP OF DEGREE 5

Marcel Herzog; Patrizia Longobardi; Mercede Maj

doi:10.3336/gm.58.2.10

ON GROUPS WITH AVERAGE ELEMENT ORDERS EQUAL TO THE AVERAGE ELEMENT ORDER OF THE ALTERNATING GROUP OF DEGREE 5

Marcel Herzog, Patrizia Longobardi, Mercede Maj

School of Mathematical Sciences

University of Salerno

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Let G be a finite group. Denote by ψ(G) the sum ψ(G) = x∈G |x|, where |x| denotes the order of the element x, and by o(G) the average element orders, i.e. the quotient (formula presented). We prove that (formula presented) if and only if (formula presented), where A₅ is the alternating group of degree 5.

Original language	English
Pages (from-to)	307-315
Number of pages	9
Journal	Glasnik Matematicki
Volume	58
Issue number	2
DOIs	https://doi.org/10.3336/gm.58.2.10
State	Published - 2023

Funding

Funders	Funder number
GNSAGA-INDAM
Istituto Nazionale di Alta Matematica "Francesco Severi"
Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni

Keywords

Group element orders
alternating group

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10.3336/gm.58.2.10

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abstract = "Let G be a finite group. Denote by ψ(G) the sum ψ(G) = x∈G |x|, where |x| denotes the order of the element x, and by o(G) the average element orders, i.e. the quotient (formula presented). We prove that (formula presented) if and only if (formula presented), where A5 is the alternating group of degree 5.",

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AU - Maj, Mercede

PY - 2023

Y1 - 2023

N2 - Let G be a finite group. Denote by ψ(G) the sum ψ(G) = x∈G |x|, where |x| denotes the order of the element x, and by o(G) the average element orders, i.e. the quotient (formula presented). We prove that (formula presented) if and only if (formula presented), where A5 is the alternating group of degree 5.

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KW - alternating group

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ON GROUPS WITH AVERAGE ELEMENT ORDERS EQUAL TO THE AVERAGE ELEMENT ORDER OF THE ALTERNATING GROUP OF DEGREE 5

Abstract

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Keywords

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