TY - JOUR
ID - 2984
TI - All simple groups with order from 1 million to 5 million are efficient
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Campbell, Colin M.
AU - Havas, George
AU - Ramsay, Colin
AU - Robertson, Edmund F.
AD - School of Mathematics and Statistics, University of St Andrews
AD - Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering,
The University of Queensland
AD - Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering,
The University of Queensland
Y1 - 2014
PY - 2014
VL - 3
IS - 1
SP - 17
EP - 30
KW - Efficient presentations
KW - simple groups
KW - coset enumeration
DO - 10.22108/ijgt.2014.2984
N2 - 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.
UR - https://ijgt.ui.ac.ir/article_2984.html
L1 - https://ijgt.ui.ac.ir/article_2984_1966833cf149fe7e096cd9874914cd5c.pdf
ER -