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Rank 3 permutation characters and maximal subgroups

  • Hung P. Tong-Viet EMAIL logo
Published/Copyright: January 3, 2013

Abstract.

Let G be a transitive permutation group acting on a finite set and let P be the stabilizer in G of a point in . We say that G is primitive rank 3 on if P is maximal in G and P has exactly three orbits on . For any subgroup H of G, we denote by the permutation character (or permutation module) over of G on the cosets . Let H and K be subgroups of G. We say if is a character of G. Also a finite group G is called nearly simple primitive rank 3 on if there exists a quasi-simple group L such that and G acts as a primitive rank 3 permutation group on the cosets of some subgroup of L. In this paper we classify all maximal subgroups M of a nearly simple primitive rank 3 group G of type , , acting on an L-orbit of non-singular points of the natural module for L such that , where P is the stabilizer of a non-singular point in . This result has an application to the study of minimal genera of algebraic curves which admit group actions.

Received: 2010-07-23
Revised: 2010-12-04
Published Online: 2013-01-03
Published in Print: 2013-01-01

© 2013 by Walter de Gruyter Berlin Boston

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