Luigi Iorio

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math.GR2026

On the Hamiltonicity of generating graphs of almost simple groups

Luigi Iorio

The generating graph $Γ (G)$ of a finite group $G$ has vertex set $G ∖ {1}$ , and two distinct vertices are adjacent if and only if they generate $G$ . Breuer, Guralnick, Lucc…

math.GR2026

Finite groups with a large normalized sum of element orders

Luigi Iorio, Marco Trombetti

For a finite group $G$ , let $ψ (G)$ be the sum of the orders of its elements, and define the corresponding normalized sum as $ψ^{'} (G) := ψ (G) / ψ (C_{∣ G ∣})$ , where $\mathcal{C}…