Year: 2011
Type: article
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.
Source: Forum Mathematicum
Author: Hung P. Tong-Viet
Institution: University of KwaZulu-Natal
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2063595757