From the 1 of 5 linked papers with an AI index.
5 papers
Fixed-point-free elements in two-orbit permutation groups
Jessica Anzanello, Sean Eberhard
The paper proves that any permutation group with exactly two orbits on more than two points must contain either a derangement or an element of prime‑power order fixing exactly one…
Diameter bounds for arbitrary finite groups and applications
Sean Eberhard, Elena Maini, Luca Sabatini +1
We prove a strong general-purpose bound for the diameter of a finite group depending only on the diameters of its composition factors and the maximal exponent of a normal abelian s…
Expanding groups with large diameter
Sean Eberhard, Luca Sabatini
We study how the spectral gap and diameter of Cayley graphs depend strongly on the choice of generating set. We answer a question of Pyber and Szabó (2013) by exhibiting a sequenc…
Examples of diameter-2 graphs with no triangle or
Sean Eberhard, Vladislav Taranchuk, Craig Timmons
For each let denote the class of graphs other than stars that have diameter and contain neither a triangle nor a . The famous Hoffman--Singleton Theore…
Probabilistic construction of some extremal -groups
Sean Eberhard, Luca Sabatini
A -group is called *ab-maximal* if for every proper subgroup of . Similarly, is called *-maximal* if for every proper subgrou…