Mariapia Moscatiello

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20172021

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math.GR2021

Base sizes of primitive permutation groups

Mariapia Moscatiello, Colva M. Roney-Dougal

Let G be a permutation group, acting on a set Ωof size n. A subset B of Ωis a base for G if the pointwise stabilizer G_(B) is trivial. Let b(G) be the minimal size of a base for G.…

math.GR2021

Primitive permutation IBIS groups

Andrea Lucchini, Marta Morigi, Mariapia Moscatiello

Let $G$ be a finite permutation group on $Ω$ . An ordered sequence of elements of $Ω$ , $(ω_{1}, \dots, ω_{t})$ , is an irredundant base for $G$ if the pointwise stabilizer $G_{(ω_1,\dots,…

math.GR2019

Boolean lattices in finite alternating and symmetric groups

Andrea Lucchini, Mariapia Moscatiello, Sebastien Palcoux +1

Given a group $G$ and a subgroup $H$ , we let $O_{G} (H)$ denote the lattice of subgroups of $G$ containing $H$ . This paper provides a classification of the subgroups $H$ of…

math.GR2019

Bounding the maximal size of independent generating sets of finite groups

Andrea Lucchini, Mariapia Moscatiello, Pablo Spiga

Denote by $m (G)$ the largest size of a minimal generating set of a finite group $G$ . We estimate $m (G)$ in terms of $\sum_{p \in π (G)} d_{p} (G),$ where we are denoting by $d_{p} (G)$ the…

math.GR2019

A polynomial bound for the number of maximal systems of imprimitivity of a finite transitive permutation group

Andrea Lucchini, Mariapia Moscatiello, Pablo Spiga

We show that, there exists a constant $a$ such that, for every subgroup $H$ of a finite group $G$ , the number of maximal subgroups of $G$ containing $H$ is bounded above by $a|G:H|…

math.GR2017

The expected number of elements to generate a finite group with $d$ -generated Sylow subgroups

Andrea Lucchini, Mariapia Moscatiello

Given a finite group $G,$ let $e (G)$ be expected number of elements of $G$ which have to be drawn at random, with replacement, before a set of generators is found. If all the Sylow…

Base sizes of primitive permutation groups

Primitive permutation IBIS groups

Boolean lattices in finite alternating and symmetric groups

Bounding the maximal size of independent generating sets of finite groups

A polynomial bound for the number of maximal systems of imprimitivity of a finite transitive permutation group

The expected number of elements to generate a finite group with d-generated Sylow subgroups

The expected number of elements to generate a finite group with $d$ -generated Sylow subgroups