On transitive sets of derangements in primitive groups
Abstract
Abstract We construct a primitive permutation action of the Steinberg triality group "Equation missing" of degree 4, 064, 256 and show that there are distinct points $$\alpha ,\beta $$ α , β such that there is no derangement "Equation missing" with $$\alpha ^g=\beta $$ α g = β . This answers a question by John G. Thompson (Problem 8.75 in the Kourovka Notebook) in the negative.
Fields of Study & Subjects
Geometric and Algebraic Topology
Advanced Topology and Set Theory
Advanced Algebra and Geometry
Publication details
- Journal / source
- Archiv der Mathematik
- Publisher
- Springer Science and Business Media LLC
- Volume
- 126
- Issue
- 6
- Pages
- 551–556
- Publication date
- 20 April 2026
- Language
- EN