Andrea Lucchini

activity

20232026

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Showing 2026 · math.GRShow all

4 papers · 2 filters

math.GR2026

Bounded-orbit lattice representations of finite groups

JiaLi Du, Andrea Lucchini, Joy Morris +1

For a finite group $G$ , let $λ (G)$ denote the minimum number of orbits on the elements of a finite lattice $L$ with $Aut (L) ≅ G$ . Babai and Goodman conjectured th…

math.GR2026

Virtually generating graphs of pro- $p$ groups

Yiftach Barnea, Andrea Lucchini, Margherita Piccolo +1

We study the virtually generating graph of pro- $p$ groups. We show that various classes of pro- $p$ groups have connected virtually generating graph and we bound its diameter in the…

math.GR2026

Supersoluble groups and the probability of generating a supersoluble subgroup

Andrea Lucchini

Let $G$ be a finite group and let $P_{U} (G)$ denote the probability that two randomly chosen elements of $G$ generate a supersoluble subgroup. We prove that if $…

math.GR2026

Sectionally indecomposable groups

Andrea Lucchini, Nowras Otmen

We introduce the notion of sectional indecomposability and study it for finite groups: a group $H$ is sectionally indecomposable if, whenever $H$ is a section of a direct product $…

Bounded-orbit lattice representations of finite groups

Virtually generating graphs of pro-p groups

Supersoluble groups and the probability of generating a supersoluble subgroup

Sectionally indecomposable groups

Virtually generating graphs of pro- $p$ groups