Cheryl E Praeger - Coprime actions of finite groups - Pure Mathematics Colloquium
| Dates: | 16 April 2021 |
|---|
| Times: | 11:00 - 12:00 |
|---|
| What is it: | Seminar |
|---|
| Organiser: | Department of Mathematics |
|---|
| Who is it for: | University staff, External researchers |
|---|
| Speaker: | Cheryl E Praeger |
|---|
|
Speaker: Cheryl E Praeger, University of Western Australia
Series: Pure Mathematics Colloquium
Title: Coprime actions of finite groups
Abstract: Gabriel Navarro asked the following question: Suppose that, for a finite linear group H acting completely reducibly on a finite vector space V, there are vectors a and b not fixed by H such that the H-orbits containing a and b have coprime lengths m and n. Is there an H-orbit on vectors 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 on V.
Viewed differently this tells us that a point-stabiliser in a finite affine primitive permutation group cannot have a pair of orbits of coprime lengths. On the other hand, stabilisers in different kinds of finite primitive permutation groups can have coprime orbits. Considering such groups led us to resolving a question of Peter Neumann from 1973, arising from a theorem of Marie Weiss n 1935. This is joint work with Silvio Dolfi, Bob Guralnick and Pablo Spiga.
Speaker
Cheryl E Praeger
Role: Speaker
Organisation: University of Western Australia
1
element country
2
- country
3
- refloc =
- gpp = http://www.columbasystems.com/customers/gpp/xml/details/1-0/
4
5
6
7
- name
- iso2
- iso3
- columbaCode
8
- code = code:GB
- name = United Kingdom
- code = http://www.columbasystems.com/customers/uom/gpp/tag/
- ns1 = http://www.columbasystems.com/customers/gpp/xml/details/1-0/
9
country name = United Kingdom
ISO2 = GB
ISO3 = GBR
Travel and Contact Information
