7 papers · 1 filter
On the connectivity of the generating and rank graphs of finite groups
Andrea Lucchini, Daniele Nemmi
The generating graph encodes how generating pairs are spread among the elements of a group. For more than ten years it has been conjectured that this graph is connected for every f…
Abelian supplements in almost simple groups
Mauro Costantini, Andrea Lucchini, Daniele Nemmi
Let be a finite almost simple group with socle . In this paper we prove that whenever is abelian, then there exists an abelian subgroup of such that $G=AG_…
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,_…
Semiregularity and connectivity of the non- graph of a finite group
Andrea Lucchini, Daniele Nemmi
Given a class of finite groups, we consider the graph whose vertices are the elements of and where two vertices are adja…
On the connectivity of the non-generating graph
Andrea Lucchini, Daniele Nemmi
Given a 2-generated finite group , the non-generating graph of has as vertices the elements of and two vertices are adjacent if and only if they are distinct and do not…
Forbidden subgraphs in generating graphs of finite groups
Andrea Lucchini, Daniele Nemmi
Let be a -generated group. The generating graph is the graph whose vertices are the elements of and where two vertices and are adjacent if $G = \langl…