SEMINAR: Groups and Combinatorics Seminar: Coprime subdegrees for primitive permutation groups and completely reducible linear groups
|Groups and Combinatorics Seminar: Coprime subdegrees for primitive permutation groups and completely reducible linear groups
Groups and Combinatorics Seminar
will speak on
Coprime subdegrees for primitive permutation groups and completely reducible linear groups
at 11am on Wednesday 7th of March in MLR2
Abstract. This work was inspired by a question of Gabriel Navarro
about orbit lengths of groups acting on finite vector spaces, and
is joint work with Pablo Spiga, Silvio Dolfi and Bob Guralnick.
If a finite group H acts irreducibly on a finite vector space V, then we proved that
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 VH
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 VH. 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. All proofs depend on the finite simple group classification.
Maths Lecture Room 2
Wed, 07 Mar 2012 11:00
Wed, 07 Mar 2012 11:45
Michael Giudici <[email protected]>
Fri, 02 Mar 2012 12:04
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