Pablo Spiga

collaborators

8 papers

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 $T$ .