JournalsggdVol. 1 , No. 4DOI 10.4171/ggd/27

Extremely primitive groups

  • Avinoam Mann

    The Hebrew University of Jerusalem, Israel
  • Cheryl E. Praeger

    The University of Western Australia, Crawley, Australia
  • Ákos Seress

    Ohio State University, Columbus, United States
Extremely primitive groups cover

Abstract

A primitive permutation group is called extremely primitive if a point stabilizer acts primitively on each of its orbits. We prove that finite extremely primitive groups are of affine type or almost simple. Moreover, we determine the affine type examples up to finitely many exceptions.