Fabio Mastrogiacomo

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20232025

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8 papers · 1 filter

math.GR2025

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 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

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.GR2024

On the minimal degree and base size of finite primitive groups

Fabio Mastrogiacomo

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

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.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 strong connectivity of the 2-Engel graphs of almost simple groups

F. Dalla Volta, F. Mastrogiacomo, P. Spiga

The Engel graph of a finite group $G$ is a directed graph encoding the pairs of elements in $G$ satisfying some Engel word. Recent work of Lucchini and the third author shows that,…