Author/Authors :
كمپبل، كالين ام. نويسنده School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, Scotland Campbell, Colin M. , هوس، جورج نويسنده Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering, The University of Queensland, Queensland 4 Havas, George , رامسي، كالين نويسنده Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering, The University of Queensland, Queensland 4 Ramsay, Colin , رابرتسون، ادموند ف. نويسنده School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, Scotland Robertson, Edmund F.
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 ecient 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.
