Finite groups with integer harmonic mean of element orders
Iulia C\u{a}t\u{a}lina Ple\c{s}ca, Marius T\u{a}rn\u{a}uceanu
TL;DR
This paper introduces a new harmonic mean function for element orders in finite groups, explores its properties, and characterizes groups where this mean is an integer.
Contribution
The paper defines a novel harmonic mean function for element orders and investigates the structure of groups with integer mean values.
Findings
Properties of the harmonic mean function are established.
Groups with integer harmonic mean are characterized.
New insights into the relationship between element orders and group structure.
Abstract
In this paper, we introduce a new function computing the harmonic mean of element orders of a finite group. We present a series of properties for this function, and then we study groups for which the value of the function is an integer.
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Taxonomy
TopicsGraph theory and applications