Sean Eberhard

collaborators

4 papers

math.GR2025

The growth of residually soluble groups

Sean Eberhard, Elena Maini

Building on work of Wilson, we show that if $G$ is a finitely generated residually soluble group whose growth function $I^^{3}$ satisfies $(lo g I^^{3} (n)) / n^{1/4} \to 0$ as $n \to \infty…

math.NT2025

Ratios of consecutive values of the divisor function

Sean Eberhard

We show that the sequence of ratios $d (n + 1) / d (n)$ of consecutive values of the divisor function attains every positive rational infinitely many times. This confirms a prediction…

math.GR2025

Intersections of Sylow 2-subgroups in symmetric groups

Sean Eberhard

We compute the asymptotic probability that a random pair of Sylow 2-subgroups in $S_{n}$ or $A_{n}$ intersects trivially. This calculation complements recent work of Diaconis, Giannell…

math.GR2025

Normal covering numbers for $S_{n}$ and $A_{n}$ and additive combinatorics

Sean Eberhard, Connor Mellon

The normal covering number $I^^{3} (G)$ of a finite group $G$ is the minimum number of proper subgroups whose conjugates cover the group. We give various estimates for $I^^{3} (S_{n})$ and $Î³…

The growth of residually soluble groups

Ratios of consecutive values of the divisor function

Intersections of Sylow 2-subgroups in symmetric groups

Normal covering numbers for Sn​ and An​ and additive combinatorics

Normal covering numbers for $S_{n}$ and $A_{n}$ and additive combinatorics