Coprime subdegrees in finite primitive groups and completely reducible linear groups
Presented by Dr. Pablo SPIGA
Type: Oral presentation
This work was inspired by a question of Gabriel Navarro about orbit lengths of groups acting on finite vector spaces. If a finite group H acts irreducibly on a finite vector space V, then for every pair of non-zero vectors, their orbit lengths a, b have a non-trivial common factor. This could be interpreted in the context of permutation groups. The group V H is an affine primitive group on V and a, b are orbit lengths of the point stabiliser H, that is, a and b are subdegrees of V H. This raises a question about subdegrees for more general primitive permutation groups. Coprime subdegrees can arise, but (we show) only for three of the eight types of primitive groups. Moreover it is never possible to have as many as three pairwise coprime subdegrees.