All simple groups with order from 1 million to 5 million are efficient

Campbell, C. M., Havas, G., Ramsay, C. and Robertson, E. F. (2014) All simple groups with order from 1 million to 5 million are efficient. International Journal of Group Theory, 3 1: 17-30.

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Author Campbell, C. M.
Havas, G.
Ramsay, C.
Robertson, E. F.
Title All simple groups with order from 1 million to 5 million are efficient
Journal name International Journal of Group Theory   Check publisher's open access policy
ISSN 2251-7650
Publication date 2014-03
Sub-type Article (original research)
Open Access Status File (Publisher version)
Volume 3
Issue 1
Start page 17
End page 30
Total pages 14
Place of publication Isfahan, Islamic Republic of Iran
Publisher University of Isfahan
Collection year 2015
Language eng
Formatted abstract
There is much interest in finding short presentations for the finite simple groups. Indeed it has been suggested that all these groups are efficient in a technical sense. In previous papers we produced nice efficient presentations for all except one of the simple groups with order less than one million. Here we show that all simple groups with order between 1 million and 5 million are efficient by giving efficient presentations for all of them. Apart from some linear groups these results are all new. We also show that some covering groups and some larger simple groups are efficient. We make substantial use of systems for computational group theory and, in particular, of computer implementations of coset enumeration to find and verify our presentations.
Keyword Efficient presentations
Simple groups
Coset enumeration
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: Official 2015 Collection
School of Information Technology and Electrical Engineering Publications
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Created: Tue, 05 Nov 2013, 18:44:46 EST by Associate Professor George Havas on behalf of School of Information Technol and Elec Engineering