A Note on Point Stabilizers in Sharp Permutation Groups of Type {0, k}

Abstract

We study sharp permutation groups of type {0, k} and observe that, once the isomorphism type of a point stabilizer is fixed, there are only finitely many possibilities for such a permutation group. We then show that a sharp permutation group of type {0, k} in which a point stabilizer is isomorphic to the alternating group on 5 letters must be a geometric group. There is, up to permutation isomorphism, one such permutation group.

Key Words:

• Finite permutation group
• Imprimitive permutation group

2010 Mathematics Subject Classification:

• 20B17

ACKNOWLEDGMENT

We thank the referee for numerous suggestions which have improved the exposition of this article.