Year: 2025
Type: article
Abstract: We treat the action of the simple group F 4 (q) on the cosets of subgroups D 4 (q), 2 D 4 (q) and 3 D 4 (q) and their extensions by graph automorphisms.We obtain the ranks and decompose the corresponding permutation characters; we show that, even allowing for the application of field automorphisms, the only two primitive multiplicity-free actions arising are those of F 4 (2) on cosets of D 4 (2).S 3 and 3 D 4 (2).3.For these two actions, we calculate the subdegrees; we find that all suborbits are self-paired, but that the action gives rise to no distance-transitive graph. MSC2020: 20G05.
Source: Pacific Journal of Mathematics
Author: R. Lawther
Institution: University of Cambridge
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4410837990