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John Britnell's Homepage

Department of Mathematics

Imperial College London

South Kensington Campus

London

SW7 2AZ

UK

email: *j.britnell@imperial.ac.uk*

I organize the LAC when it meets at Imperial College. For Autumn 2016 it will be at
City University, organised by Markus Linkelmann.

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My Research Interests

Group theory; representation theory; combinatorics
- Finite and infinite permutation groups
- Finite classical groups
- Generation of finite groups
- Coverings of groups by proper subgroups or classes of subgroups
- Generating graphs and commuting graphs of groups
- Cycle indices and generating function methods in finite groups
- Commuting probability and conjugacy probability in finite groups
- Representations of symmetric groups

#### Some current and recent projects

(This list is not comprehensive.)
- With Mark Wildon: analogues of Bell numbers which arise in the combinatorics and representation theory of Coxeter groups of types B and D
- With Ben Fairbairn and Attila Maróti: calculating the minimal sizes of subgroup coverings of finite classical groups.
- With Nick Gill: which finite almost quasisimple groups have a perfect comuting graph?
- With Neil Saunders and Tony Skyner: classifying groups of order $p$5 which have a quotient with larger minimal permutation degree.

Data [html,
PDF] on derangements of $S$_{n} acting on
$k$-sets which Mark Wildon and I computed several years ago
using MAGMA. [Each entry gives the proportion of derangements in the group in
its action on $k$-sets. The highlighted entries indicate failure of
monotonicity along the rows, which we were investigating at the time.]
The computations have been written up here.

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Links

**Some mathematical people: **
Simon Blackburn,
Peter Cameron,
Anton Evseev,
Ben Fairbairn,
Jason Fulman,
Nick Gill,
Stephen Glasby,
Bob Guralnick,
Charles Leedham-Green,
Martin Liebeck,
John MacQuarrie,
Attila Maróti,
Peter Neumann,
Eamonn O'Brien,
Cheryl Praeger,
Sarah Rees,
Amps Rattan,
Jeremy Rickard,
Neil Saunders,
Tony Skyner,
Pablo Spiga,
Mark Wildon.

**Some mathematical places: **
Bristol Maths,
Cambridge Pure Maths,
Imperial Maths,
Leeds Maths,
Newcastle Maths,
Oxford Maths Institute,
Pembroke College Cambridge,
St Anne's College Oxford,
London Mathematical Society,
MAGMA.