Andrea Lucchini

activity

20102023

most citedInvariable generation with elements of coprime prime-power order

2 citations · 2 across the 7 of their papers we have counts for

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6 papers · 1 filter

math.GR2023

Probabilistic properties of profinite groups

Eloisa Detomi, Andrea Lucchini, Marta Morigi +1

Let $C$ be a class of finite groups which is closed for subgroups, quotients and direct products. Given a profinite group $G$ and an element $x \in G$ , we denote by $P_{\m…

math.GR2022

Strongly generating elements in finite and profinite groups

Eloisa Detomi, Andrea Lucchini

Given a finite group $G$ and an element $g \in G$ , we may compare the expected number $e (G)$ of elements needed to generate $G$ and the expected number $e (G, g)$ of elements of $G$ n…

math.GR2017

The diameter of the generating graph of a finite soluble group

Andrea Lucchini

Let $G$ be a finite 2-generated soluble group and suppose that $⟨ a_{1}, b_{1} ⟩ = ⟨ a_{2}, b_{2} ⟩ = G$ . If either $G^{'}$ is of odd order or $G^{'}$ is nilpotent, t…

math.GR2014

Coprime invariable generation and minimal-exponent groups

Eloisa Detomi, Andrea Lucchini, Colva M. Roney-Dougal

A finite group $G$ is \emph{coprimely-invariably generated} if there exists a set of generators ${g_{1}, ..., g_{u}}$ of $G$ with the property that the orders $∣ g_{1} ∣, ..., ∣ g_{u} ∣$ are…

math.GR2014

Invariable generation of prosoluble groups

Eloisa Detomi, Andrea Lucchini

A group $G$ is invariably generated by a subset $S$ of $G$ if $G = s^{g (s)} ∣ s \in S$ for each choice of $g (s) \in G$ , $s \in S$ . Answering two questions posed by Kantor, Lubotzk…

math.GR2014★ 2 cited

Invariable generation with elements of coprime prime-power order

Eloisa Detomi, Andrea Lucchini

A finite group $G$ is coprimely-invariably generated if there exists a set of generators ${g_{1}, \dots, g_{d}}$ of $G$ with the property that the orders $∣ g_{1} ∣, \dots, ∣ g_{d} ∣$ are…