Sean Eberhard

collaborators

6 papers

math.GR2026

Forcible groups and Frattini covers

Sean Eberhard, Robert M. Guralnick, Carl Schildkraut +1

We say that a finite group $G$ *forces* a finite group $H$ if every finite cover of $G$ contains a subgroup isomorphic to $H$ , and we say $H$ is *forcible* if some finite group $G$ …

math.GR2026

Fixed-point-free elements in two-orbit permutation groups

Jessica Anzanello, Sean Eberhard

Let $G$ be a two-orbit permutation group on $n > 2$ points. We show that $G$ contains either a derangement or an element of prime-power order with a unique fixed point. As a coroll…

math.GR2026

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…

math.GR2026

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 sequence…

math.CO2025

Examples of diameter-2 graphs with no triangle or $K_{2, t}$

Sean Eberhard, Vladislav Taranchuk, Craig Timmons

For each $t \geq 1$ let $W_{t}$ denote the class of graphs other than stars that have diameter $2$ and contain neither a triangle nor a $K_{2, t}$ . The famous Hoffman--Singleton Theore…

math.GR2025

Probabilistic construction of some extremal $p$ -groups

Sean Eberhard, Luca Sabatini

A $p$ -group $G$ is called *ab-maximal* if $∣ H : H^{'} ∣ < ∣ G : G^{'} ∣$ for every proper subgroup $H$ of $G$ . Similarly, $G$ is called * $d$ -maximal* if $d (H) < d (G)$ for every proper subgrou…

Forcible groups and Frattini covers

Fixed-point-free elements in two-orbit permutation groups

Diameter bounds for arbitrary finite groups and applications

Expanding groups with large diameter

Examples of diameter-2 graphs with no triangle or K2,t​

Probabilistic construction of some extremal p-groups

Examples of diameter-2 graphs with no triangle or $K_{2, t}$

Probabilistic construction of some extremal $p$ -groups