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math.GR2024
On finite groups whose power graph is claw-free
Pallabi Manna, Santanu Mandal, Andrea Lucchini
A graph is called claw-free if it contains no induced subgraph isomorphic to the complete bipartite graph . The undirected power graph of a group has vertices the ele…
math.GR2024
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…
math.GR2024
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_…