Rank 3 permutation characters and maximal subgroups

TL;DR

This paper classifies maximal subgroups of certain rank 3 groups related to orthogonal groups over finite fields, with implications for algebraic curve symmetries.

Contribution

It provides a complete classification of maximal subgroups satisfying a specific permutation character condition for nearly simple rank 3 groups of type Omega.

Findings

Classified all such maximal subgroups for the specified groups.

Established a connection between subgroup structure and algebraic curve automorphisms.

Applied results to minimal genus problems of algebraic curves.

Abstract

In this paper we classify all maximal subgroups M of a nearly simple primitive rank 3 group G of type L=Omega_{2m+1}(3), m > 3; acting on an L-orbit E of non-singular points of the natural module for L such that 1_P^G <=1_M^G where P is a stabilizer of a point in E. This result has an application to the study of minimal genera of algebraic curves which admit group actions.