A characterization ofPSp(2m,q) andPΩ(2m+ 1,q) as rank 3 permutation groups

Finite permutation groups of rank 3

By the rank of a transitive permutation group we mean the number of orbits of the stabilizer of a point thus rank 2 means multiple transitivity. Interest is drawn to the simply transitive groups of "small" rank > 2 by the fact that every known finite simple group admits a representation as a primitive group of rank at most 5 while not all of these groups have doubly transitive representations. ...

On imprimitive rank 3 permutation groups

A classification is given of rank 3 group actions which are quasiprimitive but not primitive. There are two infinite families and a finite number of individual imprimitive examples. When combined with earlier work of Bannai, Kantor, Liebler, Liebeck and Saxl, this yields a classification of all quasiprimitive rank 3 permutation groups. Our classification is achieved by first classifying imprimi...

Rank 3 Permutation Modules of the Finite Classical Groups

The cross-characteristic permutation modules for the actions of the finite classical groups on singular 1-spaces of their natural modules are studied. The composition factors and submodule lattices are determined.

Characterization of Families of Rank 3 Permutation Groups by the Subdegrees II 1)

The conditions on N can be replaced by the assumption tha t N is at least 6 and the intersection number/~ has the value ( q § 1) 2. The cases N----4 and 5 are unsettled even under the assumption tha t /~ has this value. We number the main theorems of this sequences of papers consecutively, Theorems I and I I having appeared in [4]. Theorem I I I can be regarded as a linear analogue of Theorem I...

Characterization of Families of Rank 3 Permutation Groups by the Subdegrees I