E. O'Brien

activity

20152025

most citedRegular orbits of symmetric and alternating groups

15 citations · 26 across the 15 of their papers we have counts for

collaborators

16 papers

math.GR2025

Elusive groups from non-split extensions

Jiyong Chen, Melissa Lee, Dorde Mitrovic +2

A finite transitive permutation group is elusive if it contains no derangements of prime order. These groups are closely related to a longstanding open problem in algebraic graph t…

math.GR2025

Categorification of characteristic structures

Peter A. Brooksbank, Heiko Dietrich, Joshua Maglione +2

We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing o…

math.GR2024

Exceptional groups of order $p^{6}$ for primes $p \geq 5$

E. A. O'Brien, Sunil Kumar Prajapati, Ayush Udeep

The minimal faithful permutation degree $μ (G)$ of a finite group $G$ is the least integer $n$ such that $G$ is isomorphic to a subgroup of the symmetric group $S_{n}$ . If $G$ has a n…

math.GR2023★ 1 cited

Minimal degrees for faithful permutation representations of groups of order $p^{6}$ where $p$ is an odd prime

E. A. O'Brien, Sunil Kumar Prajapati, Ayush Udeep

We determine the minimal degree of a faithful permutation representation for each group of order $p^{6}$ where $p$ is an odd prime. We also record how to obtain such a representation…

math.AG2023

Local systems and Suzuki groups

L. Alpoge, N. M. Katz, G. Navarro +2

We study geometric monodromy groups $G_{\geo,\sF_q}$ of the local systems $\sF_q$ on the affine line over $\F_2$ of rank $D = q (q - 1)$ , $q = 2^{2 n + 1}$ , constructed in \cite{Ka-ER…

math.GR2023

Isomorphism invariant metrics

P. A. Brooksbank, J. F. Maglione, E. A. O'Brien +1

Within a category $C$ , having objects $C_{0}$ , it may be instructive to know not only that two objects are non-isomorphic, but also how far from being isomorphic th…