Presenters: Cheryl Praeger, UWA

Let H be a finite linear group acting completely reducibly on a finite vector space V. Gabriel Navarro asked: if the H-orbits containing vectors a and b have coprime lengths m and n, is there an H-orbit of length mn? We answered, by showing that the H-orbit containing a + b has length mn, and by showing, moreover, that in this situation H cannot be irreducible. That is to say, a stabiliser in an affine primitive permutation group does not have a pair of orbits of coprime lengths. I will make some comments about coprime orbit lengths for stabilisers in arbitrary primitive permutation groups. This is joint work with Silvio Dolfi, Bob Guralnick and Pablo Spiga.

### About Maths Colloquium

The Mathematics Colloquium is directed at students and academics working in the fields of pure and applied mathematics, and statistics.

We aim to present expository lectures that appeal to our wide audience.

Information for speakers

#### Information for speakers

Maths colloquia are usually held on Mondays, from 2pm to 3pm, in various locations at St Lucia.

Presentations are 50 minutes, plus five minutes for questions and discussion.

Available facilities include:

- computer
- data projector
- chalkboard or whiteboard

To avoid technical difficulties on the day, please contact us in advance of your presentation to discuss your requirements.