Groups, Geometry, and Dynamics

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Volume 1, Issue 4, 2007, pp. 623–660
DOI: 10.4171/GGD/27

Published online: 2007-12-31

Extremely primitive groups

Avinoam Mann[1], Cheryl E. Praeger[2] and Ákos Seress[3]

(1) The Hebrew University of Jerusalem, Israel
(2) The University of Western Australia, Crawley, Australia
(3) Ohio State University, Columbus, United States

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.

Keywords: Primitive permutation groups

Mann Avinoam, Praeger Cheryl, Seress Ákos: Extremely primitive groups. Groups Geom. Dyn. 1 (2007), 623-660. doi: 10.4171/GGD/27