Pablo Spiga

activity

20152026

collaborators

20 papers

math.GR2026

Bounded-orbit lattice representations of finite groups

JiaLi Du, Andrea Lucchini, Joy Morris +1

For a finite group $G$ , let $λ (G)$ denote the minimum number of orbits on the elements of a finite lattice $L$ with $Aut (L) ≅ G$ . Babai and Goodman conjectured th…

math.CO2026

An equivalence between a conjecture of Neumann-Praeger on Kronecker classes and a conjecture on cliques of derangement graphs

Jessica Anzanello, Pablo Spiga

We prove an equivalence between a conjecture of Neumann and Praeger on Kronecker classes in algebraic number fields, and a conjecture on cliques of derangement graphs in combinator…

math.GR2025

On the density of Sylow numbers

Andrea Lucchini, Pablo Spiga

Let $p$ be a prime number. We say that a positive integer $n$ is a Sylow $p$ -number if there exists a finite group having exactly $n$ Sylow $p$ -subgroups. When $p = 2$ , every odd int…

math.GR2025

Finite simple groups have many classes of prime order elements

Jessica Anzanello, Pablo Spiga

Let $T$ be a finite non-abelian simple group. Giudici, Morgan and Praeger have shown that the order of $T$ is bounded above by a function depending on the maximum number of $\mathr…

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.GR2025

On the base size and minimal degree of transitive groups

Lorenzo Guerra, Attila Maróti, Fabio Mastrogiacomo +1

Let $G$ be a permutation group, and denote with $μ (G)$ and $b (G)$ its minimal degree and base size respectively. We show that for every $ε > 0$ , there exists a transitive p…

math.GR2025

The maximal rank of a string group generated by involutions for alternating groups

Jessica Anzanello, Maria Elisa Fernandes, Pablo Spiga

A string group generated by involutions, or SGGI, is a pair $Γ = (G, S)$ , where $G$ is a group and $S = {ρ_{0}, \dots, ρ_{r - 1}}$ is an ordered set of involutions generating $G$ and sat…

math.GR2025

Counting subgroups of a finite group containing a prescribed subgroup

Lorenzo Guerra, Fabio Mastrogiacomo, Pablo Spiga

Let $R$ be a finite group, and let $T$ be a subgroup of $R$ . We show that there are at most \[ 7.3722[R:T]^{\frac{\log_2[R:T]}{4}+1.8919} \] subgroups of $R$ containing $T$ .

math.GR2025

Normal subgroups and permutation characters: a correction to a proof of Klingen

Peter Muller, Pablo Spiga

Let $G$ be a finite group. For subgroups $U$ and $V$ let $1_{U}^{G}$ and $1_{V}^{G}$ be the permutation characters for the action of $G$ on the right cosets of $U$ and $V$ , respectively. L…

math.GR2025

Commutators between coprime order elements in non-abelian simple groups

Andrea Lucchini, Pablo Spiga

Recent investigations on the set of commutators between the elements of a finite group having relatively prime orders have prompt us to propose a variant of the Ore conjecture: For…

math.CO2025

Kronecker classes and cliques in derangement graphs

Marina Cazzola, Louis Gogniat, Pablo Spiga

Given a permutation group $G$ , the derangement graph of $G$ is defined with vertex set $G$ , where two elements $x$ and $y$ are adjacent if and only if $x y^{- 1}$ is a derangement. W…

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

IBIS primitive groups of almost simple type

Fabio Mastrogiacomo, Pablo Spiga

Let $G$ be a finite permutation group on $Ω$ . An ordered sequence $(ω_{1} \dots, ω_{ℓ})$ of elements of $Ω$ is an irredundant base for $G$ if the pointwise stabilizer is trivial and…

math.CO2024

Haar graphical representations of finite groups and an application to poset representations

Joy Morris, Pablo Spiga

Let $R$ be a group and let $S$ be a subset of $R$ . The Haar graph $Haar (R, S)$ of $R$ with connection set $S$ is the graph having vertex set $R \times {- 1, 1}$ , where two di…

math.GR2024

On the structure of the character degree graphs having diameter three

Silvio Dolfi, Roghayeh Hafezieh, Pablo Spiga

The structure of the character degree graphs $Δ (G)$ , i.e. the prime graphs on the set $cd (G)$ of the irreducible character degrees of a finite group $G$ , such that $G$ is…

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

On the cardinality of irredundant and minimal bases of finite permutation groups

Francesca Dalla Volta, Fabio Mastrogiacomo, Pablo Spiga

Given a finite permutation group $G$ with domain $Ω$ , we associate two subsets of natural numbers to $G$ , namely $I (G, Ω)$ and $M (G, Ω)$ , which are the sets of ca…

math.GR2023

On the diameter of Engel graphs

Andrea Lucchini, Pablo Spiga

Given a finite group $G$ , the Engel graph of $G$ is a directed graph $Γ (G)$ encoding pairs of elements satisfying some Engel word. Namely, $Γ (G)$ is the directed graph, where the v…

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.GR2015

Bipartite divisor graph for the set of irreducible character degrees

Roghayeh Hafezieh

Let $G$ be a finite group. We consider the set of the irreducible complex characters of $G$ , namely $I r r (G)$ , and the related degree set $c d (G) = {χ (1) : χ \in I r r (G)}$ . Let $ρ (G)$ …