Alternating and symmetric groups with Eulerian generating graph

Andrea Lucchini, Claude Marion

Maximal subgroups of finite soluble groups in general position

Eloisa Detomi, Andrea Lucchini

Generating sets of finite groups

Peter J. Cameron, Andrea Lucchini, Colva M. Roney-Dougal

Rationality of the probabilistic zeta function of finitely generated profinite groups

Duong Hoang Dung, Andrea Lucchini

Rings as the unions of proper subrings

Andrea Lucchini, Attila Maroti

On the orders of the non-Frattini elements of a finite group

Andrea Lucchini

A finiteness condition on the coefficients of the probabilistic zeta function

Duong Hoang Dung, Andrea Lucchini

The generating graph of the abelian groups

Cristina Acciarri, Andrea Lucchini

Finite groups with planar generating graph

Andrea Lucchini

The paper classifies all finite 2‑generated groups whose generating graph is planar, showing that only a short list of small groups (e.g., C₂, C₃, C₄, C₅, C₆, C₂×C₂, D₃, D₄, Q₈, C₄…

Finite groups with large Chebotarev invariant

Andrea Lucchini, Gareth Tracey

Invariable generation with elements of coprime prime-power order

Eloisa Detomi, Andrea Lucchini

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

Andrea Lucchini, Mariapia Moscatiello

Invariable generation of prosoluble groups

Eloisa Detomi, Andrea Lucchini

Intersection of maximal subgroups in prosolvable groups

Iker de las Heras, Andrea Lucchini

The diameter of the generating graph of a finite soluble group

Andrea Lucchini

A bound on the expected number of random elements to generate a finite group all of whose Sylow subgroups are d-generated

Andrea Lucchini

The Chebotarev invariant of a finite group: a conjecture of Kowalski and Zywina

Andrea Lucchini

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

Andrea Lucchini, Mariapia Moscatiello, Pablo Spiga

Characterization of finitely generated infinitely iterated wreath products

Eloisa Detomi, Andrea Lucchini

Maximal irredundant families of minimal size in the alternating group

Martino Garonzi, Andrea Lucchini

Bounding the maximal size of independent generating sets of finite groups

Andrea Lucchini, Mariapia Moscatiello, Pablo Spiga

The authors bound the maximal size of a minimal generating set of a finite group using the sum of the minimal numbers of generators of its Sylow subgroups.

Covers and Normal Covers of Finite Groups

Andrea Lucchini, Martino Garonzi

Direct products of finite groups as unions of proper subgroups

Andrea Lucchini, Martino Garonzi

Irredundant and minimal covers of finite groups

Andrea Lucchini, Martino Garonzi

Coprime invariable generation and minimal-exponent groups

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