S. Glasby

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20242026

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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…

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

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

Finite $2$ -groups with exactly three automorphism orbits