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SEMINAR: Groups and Combinatorics Seminar: Coprime subdegrees for primitive permutation groups and completely reducible linear groups

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Groups and Combinatorics Seminar: Coprime subdegrees for primitive permutation groups and completely reducible linear groups Other events...
Groups and Combinatorics Seminar

Cheryl Praeger(UWA)

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.
Speaker(s) Cheryl Praeger
Location Maths Lecture Room 2
Contact Michael Giudici <[email protected]>
Start Wed, 07 Mar 2012 11:00
End Wed, 07 Mar 2012 11:45
Submitted by Michael Giudici <[email protected]>
Last Updated Fri, 02 Mar 2012 12:04
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