Details of Grant 

EPSRC Reference:	GR/R95265/01
Title:	Computing in the Fischer-Griess Monster
Principal Investigator:	Wilson, Professor R
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	School of Mathematics
Organisation:	University of Birmingham
Scheme:	Standard Research (Pre-FEC)
Starts:	01 May 2002	Ends:	30 April 2004	Value (£):	111,419
EPSRC Research Topic Classifications:	Algebra & Geometry Logic & Combinatorics
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
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Panel History:
Summary on Grant Application Form
The theory of finite groups is of central importance in mathematics, and finds wide applications in all the physical sciences and elsewhere. The building blocks of finite groups are the 'simple' groups, which fall into well understood families, and twenty-six 'sporadic' exceptions, the largest and most interesting of which is the Monster, which has attracted enormous interest. Attention is now focussed on studying properties of these groups, especially their maximal subgroups, and their Brauer characters. Computation continues to play an important role in the investigation of all the sporadic simple groups, generally by representing elements of the groupas permutations or matrices. Unfortunately, the Monster is far too big, and existing methods will not extend directly to this group. In this project a more mathematically sophisticated approach is taken. We do not store the group generators as huge matrices, but as subroutines which compute the images of vectors directly. This approach necessitates a complete re-thinking of the methods for solving standard problems.The aims of the project are (a) to develop software for computing in the Monster, (b) to make progress in determining the maximal subgroups of the Monster, and (c) to answer other interesting questions about the Monster.Keywords: Mathematics, Computing, Software Engineering, Information Technology, Computational Group Theory, Sporadic Groups, The Monster, Maximal Subgroups
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Organisation Website:	http://www.bham.ac.uk