Rank 3 permutation characters and maximal subgroups

作者：Tong Viet Hung P^*

来源：Forum Mathematicum, 2013, 25(1): 49-106.

DOI：10.1515/FORM.2011.106

• Permutation characters
• nearly simple groups
• maximal subgroups

Let G be a transitive permutation group acting on a finite set G and let P be the stabilizer in G of a point in G. We say that G is primitive rank 3 on G if P is maximal in G and P has exactly three orbits on G. For any subgroup H of G, we denote by 1(H)(G) the permutation character (or permutation module) over C of G on the cosets G/H. Let H and K be subgroups of G. We say 1(H)(G) %26lt;= 1(K)(G) if 1(K)(G) - 1(H)(G) is a character of G. Also a finite group G is called nearly simple primitive rank 3 on G if there exists a quasi-simple group L such that L/Z(L) (sic) G/Z(L) %26lt;= Aut(L/Z(L)) 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 L = Omega(2m+1) (3), m %26gt;= 3, acting on an L-orbit E of non-singular points of the natural module for L such that 1(P)(G) %26lt;= 1(M)(G), where P is the stabilizer of a non-singular point in G. This result has an application to the study of minimal genera of algebraic curves which admit group actions.

• 出版日期2013-1