Sean Eberhard

works on

derangements 1 normal 2-coverings 1 permutation groups 1 simple groups 1 two-orbit actions 1

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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

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…

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 SzabÃ³ (2013) by exhibiting a sequenc…

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

Probabilistic construction of some extremal p-groups

Probabilistic construction of some extremal $p$ -groups