Fabio Mastrogiacomo

activity

20242026

collaborators

6 papers

math.GR2026

Finite groups in which every proper characteristic subgroup is cyclic

Marco Damele, Fabio Mastrogiacomo

Let $G$ be a finite non-cyclic, non-characteristically simple group with the property that all proper characteristic subgroups of $G$ are cyclic. We call such a group $\mathrm{CCS}…

math.GR2025

On the base size and minimal degree of transitive groups

Lorenzo Guerra, Attila MarÃ³ti, Fabio Mastrogiacomo +1

Let $G$ be a permutation group, and denote with $I^¼ (G)$ and $b (G)$ its minimal degree and base size respectively. We show that for every $ε > 0$ , there exists a transitive…

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

IBIS primitive groups of almost simple type

Fabio Mastrogiacomo, Pablo Spiga

Let $G$ be a finite permutation group on $I^c ◯$ . An ordered sequence $(I ¨ _{1} \dots, I ¨ _{ℓ})$ of elements of $I^c ◯$ is an irredundant base for $G$ if the pointwise stabilizer is trivial…

math.GR2024

On the minimal degree and base size of finite primitive groups

Fabio Mastrogiacomo

Let $G$ be a finite permutation group acting on $I^c ◯$ . A base for $G$ is a subset $B \subseteq I^c ◯$ such that the pointwise stabilizer $G_{(B)}$ is the identity. The base size of $G$ …

math.GR2024

Cardinalities of irredundant bases of finite primitive groups

Fabio Mastrogiacomo

Let $G$ be a finite permutation group acting on a set $I^c ◯$ . An ordered sequence $(I ¨ _{1}, \dots, I ¨ _{ℓ})$ of elements of $I^c ◯$ is an irredundant base for $G$ if the pointwise stabiliz…