# John Bray’s research

My research is in the areas of Algebra and Combinatorics. Currently, I am working on the www-ATLAS of Finite Group Representations. My research covers many areas, some of which are related to the www-ATLAS. These include:
• Symmetric generation, symmetric presentations, and presentations.
• Faithful representations of p-local subgroups of sporadic groups in characteristic p.
• Characteristic 0 representations.
• Algorithms in finite groups, including group recognition (sometimes).
• Finite groups applied to graphs.
• Maximal subgroups of finite classical groups and their extensions.
• Other things.
More detailed descriptions of my research will be given below. I am still in the process of writing it.
My list of publications, and the papers themselves will be available here. At the moment, my Birmingham pages are more informative.

### Symmetric generation, symmetric presentations, and presentations

My PhD was on symmetric presentations of some finite groups, including the sporadic groups HN, McL and Ly. I have also done research in this topic since my PhD.

### Matrix representations of finite (mostly) groups

#### Representations of p-local groups in characteristic p

The best way to do it.

#### Characteristic 0 representations

Just like it says on the tin. Includes research into reducing the size of integers in the resulting representation. I am also interested in effective (or rather ‘nice&rsquo) orthogonalisation or unitarisation of representations. (One can always use Gram–Schmidt orthonormalisation to do this, but one can expect the result to be quite nauseous, particularly the huge amount of irrationalities that crop up in the representation after such a process.)

### Algorithms in finite groups, including group recognition

Obviously my involution centraliser method comes under this section. As does my double coset enumerator.

### Finite groups applied to graphs

These are mainly highly symmetric cubic graphs. The more arc-transitive the better. The so-called sextet graphs are at least 4-arc transitive.

### Other things

Rob Wilson and I have found some constructions for producing finite groups with few automorphisms. In fact |Aut(G)| / φ(|G|) can be made arbitrarily small, even if we restrict G to being perfect, or soluble.
R.A.Wilson (same person as above), J.S.Wilson and I have found a characterisation of finite soluble by laws in 2 variables; these laws can be defined by a simple recursion.

This page is maintained by John Bray. The views and opinions expressed in these pages are mine. The contents of these pages have not been reviewed or approved by Queen Mary, University of London.

Last updated: 24th June 2005.