Journal of the London Mathematical Society Advance Access published online on November 14, 2007
Journal of the London Mathematical Society, doi:10.1112/jlms/jdm086
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© 2007 London Mathematical Society
Symmetric presentation of the Janko group J4
School of Mathematics
The University of Birmingham
Edgbaston
Birmingham B15 2TT
United Kingdom
sean.bolt{at}tesco.net
j.n.bray{at}qmul.ac.uk
We demonstrate how readily a definition of the largest Janko group J4 follows from a primitive action of the Mathieu group M24 by exhibiting J4 as an image of the progenitor 2*3795:M24. This symmetric presentation is converted into an ordinary presentation on three generators.
2000 Mathematics Subject Classification 20D08 (primary), 20F05 (secondary).
Received August 22, 2005; revised December 7, 2006;
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