On the efficiency of the simple groups of order less than a million and their covers

Campbell, Colin M., Havas, George, Ramsay, Colin and Robertson, Edmund F. (2007) On the efficiency of the simple groups of order less than a million and their covers. Experimental Mathematics, 16 3: 347-358. doi:10.1080/10586458.2007.10129006

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Author Campbell, Colin M.
Havas, George
Ramsay, Colin
Robertson, Edmund F.
Title On the efficiency of the simple groups of order less than a million and their covers
Journal name Experimental Mathematics   Check publisher's open access policy
ISSN 1058-6458
Publication date 2007
Sub-type Article (original research)
DOI 10.1080/10586458.2007.10129006
Volume 16
Issue 3
Start page 347
End page 358
Total pages 12
Editor R. de la Llave
Place of publication USA
Publisher A K Peters Ltd
Collection year 2008
Language eng
Subject 280405 Discrete Mathematics
780101 Mathematical sciences
C1
Abstract There is much interest in finding short presentations for the finite simple groups. In a previous paper we produced nice efficient presentations for all small simple groups and for their covering groups. Here we extend those results from simple groups of order less than 100,000 up to order one million, but we leave one simple group and one covering group for which the efficiency question remains unresolved. We give presentations that are better than what was previously available, in terms of length and in terms of computational properties, in the process answering two previously unresolved problems about the efficiency of covering groups of simple groups. Our results are based on major amounts of computation. We make substantial use of systems for computational group theory and, in particular, of computer implementations of coset enumeration.
Keyword Mathematics
efficient presentations
simple groups
covering groups
Presentations
Q-Index Code C1
Q-Index Status Confirmed Code

 
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Created: Mon, 18 Feb 2008, 15:43:51 EST