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Journal of the London Mathematical Society Advance Access originally published online on November 14, 2007
Journal of the London Mathematical Society 2007 76(3):683-701; doi:10.1112/jlms/jdm086
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© 2007 London Mathematical Society

Symmetric presentation of the Janko group J4

Sean W. Bolt, John N. Bray and Robert T. Curtis

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; published online November 14, 2007.


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