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Abstract
We prove that the simple group which has order 372000 is efficient by providing an efficient presentation for it. This leaves one simple group with order less than one million,
which has order 979200, whose efficiency or otherwise remains to be determined.
6 ACKNOWLEDGMENTS
The work in this paper was initiated while the second and third authors were in St Andrews. It was supported by EPSRC Grant GL/L21013. The second author was partially supported by the Australian Research Council. We thank Greg Gamble for help with GAP programs. We are grateful to the University of St Andrews for access to the Beowolf cluster and to The University of Queensland's High Performance Computing Unit for access to the Origin 2000 supercomputer where many major computations were performed.
Notes
An early draft of this paper was mistakenly printed in Communications in Algebra, Volume 30(2), 971–975 (2002). This is the correct version.