The Classification of Primitive Sharp Permutation Groups of Type {0, k}

Abstract

The purpose in this paper is to complete the classification of primitive sharp permutation groups of type ({0, k}, n) by proving that no such group can be almost simple.

Key Words:

• Almost simple group
• Primitive permutation group
• Sharp permutation group

2010 Mathematics Subject Classification:

• 20B10
• 20B15
• 20E32

ACKNOWLEDGMENTS

The author wishes to express his thanks to Professors Ronald Solomon and J. Matthew Douglass for valuable conversations relating to Proposition 4.1. Finally, the author would like thank the referee for numerous valuable suggestions that have greatly improved the presentation of these results.

Notes

Communicated by A. Turull.