# John Britnell's Homepage

Department of Mathematics
Imperial College London
South Kensington Campus
London
SW7 2AZ
UK

email: j.britnell@imperial.ac.uk

#### London Algebra Colloquium

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

## 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.