Fabio Mastrogiacomo

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20232025

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3 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 $T$ .