S. Glasby

activity

20242026

collaborators

5 papers

math.NT2026

Hilbert's Theorem 90, periodicity, and roots of Artin-Schreier polynomials

S. P. Glasby

Let $E / F$ be a cyclic field extension of degree $n$ , and let $I ¨ $ generate the group $Gal (E / F)$ . If $Tr_{F}^{E} (y) = \sum_{i = 0}^{n - 1} I ¨ ^{i} y = 0$ , then the additive form of Hilb…

math.GR2025

Classifying finite groups G with three Aut(G)-orbits

Stephen P. Glasby

We give a complete and irredundant list of the finite groups $G$ for which Aut $(G)$ , acting naturally on $G$ , has precisely $3$ orbits. There are 7 infinite families: one abelian,…

math.GR2025

Bipartite $q$ -Kneser graphs and two-generated irreducible linear groups

S. P. Glasby, Alice C. Niemeyer, Cheryl E. Praeger

Let $V := (F_{q})^{d}$ be a $d$ -dimensional vector space over the field $F_{q}$ of order $q$ . Fix positive integers $e_{1}, e_{2}$ satisfying $e_{1} + e_{2} = d$ . Motivated by analysi…

math.GR2025

Finite $2$ -groups with exactly three automorphism orbits

Alexander Bors, Stephen P. Glasby

We give a complete classification of the finite $2$ -groups $G$ for which the automorphism group $Aut (G)$ acting naturally on $G$ has three orbits. There are two infi…

math.RT2024

Absolutely irreducible quasisimple linear groups containing elements of order a specified Zsigmondy prime

S. P. Glasby, Alice C. Niemeyer, Cheryl E. Praeger +1

This paper is concerned with absolutely irreducible quasisimple subgroups $G$ of a finite general linear group $G L_{d} (F_{q})$ for which some element $g \in G$ of prime order $…

Hilbert's Theorem 90, periodicity, and roots of Artin-Schreier polynomials

Classifying finite groups G with three Aut(G)-orbits

Bipartite q-Kneser graphs and two-generated irreducible linear groups

Finite 2-groups with exactly three automorphism orbits

Absolutely irreducible quasisimple linear groups containing elements of order a specified Zsigmondy prime

Bipartite $q$ -Kneser graphs and two-generated irreducible linear groups

Finite $2$ -groups with exactly three automorphism orbits