13 citations · 14 across the 25 of their papers we have counts for
41 papers · 1 filter
Finite groups in which there are only two possible cardinalities for an independent generating set
Andrea Lucchini, Pablo Spiga
A generating set for a group is independent if the subgroup generated by is properly contained in , for all In this paper, we study a probl…
The Engel graph of almost simple groups
Andrea Lucchini, Pablo Spiga
Given a finite group , the Engel graph of is a directed graph encoding pairs of elements satisfying some Engel word. From the work of Detomi, Lucchini and Nemmi, the strongl…
Minimal invariable generating sets
Daniele Garzoni, Andrea Lucchini
A subset of a group invariably generates if, when each element of is replaced by an arbitrary conjugate, the resulting set generates An invariable generating s…
The Engel graph of a finite group
Eloisa Detomi, Andrea Lucchini, Daniele Nemmi
For a finite group we investigate the direct graph whose vertices are the non-hypercentral elements of and where there is an edge if and only if $[x,_…
A generalization of a question asked by B. H. Neumann
Andrea Lucchini
Let be a word and let and be two positive integers. We say that a finite group has the -property if however a set of elements and a set …
The -Möbius function of a finite group
Francesca Dalla Volta, Andrea Lucchini
The Möbius function of the subgroup lettice of a finite group has been introduced by Hall and applied to investigate several different questions. We propose the following gener…