Marco Fusari

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20232025

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6 papers · 1 filter

math.GR2025

Normal 2-coverings in affine groups of small dimension

Marco Fusari, Andrea Previtali, Pablo Spiga

A finite group $G$ admits a normal $2$ -covering if there exist two proper subgroups $H$ and $K$ with $G = ⋃_{g \in G} H^{g} \cup ⋃_{g \in G} K^{g}$ . For determining inductively the…

math.GR2024

Kronecker classes, normal coverings and chief factors of groups

Marco Fusari, Scott Harper, Pablo Spiga

For a group $G$ , a subgroup $U \leq G$ and a group $Inn (G) \leq A \leq Aut (G)$ , we say that $U$ is an $A$ -covering group of $G$ if $G = ⋃_{a \in A} U^{a}$ . A th…

math.GR2024

On derangements in simple permutation groups

Timothy C. Burness, Marco Fusari

Let $G ⩽ Sym (Ω)$ be a finite transitive permutation group and recall that an element in $G$ is a derangement if it has no fixed points on $Ω$ . Let $Δ (G)$ be the set o…

math.GR2024

Groups having minimal covering number 2 of diagonal type

Marco Fusari, Andrea Previtali, Pablo Spiga

Garonzi and Lucchini~\cite{GL} explored finite groups $G$ possessing a normal $2$ -covering, where no proper quotient of $G$ exhibits such a covering. Their investigation offered a…

math.GR2023

Cliques in derangement graphs for innately transitive groups

Marco Fusari, Andrea Previtali, Pablo Spiga

Given a permutation group $G$ , the derangement graph of $G$ is the Cayley graph with connection set the derangements of $G$ . The group $G$ is said to be innately transitive if $G$ …

math.GR2023

On the maximum number of subgroups of a finite group

Marco Fusari, Pablo Spiga

Given a finite group $R$ , we let $Sub (R)$ denote the collection of all subgroups of $R$ . We show that $∣ Sub (R) ∣ < c \cdot ∣ R ∣^{\frac{l o g _{2} ∣ R ∣}{4}}$ , where $c<7.372…