July 05, 2003
The McLaughlin Group

Not only is the McLaughlin Group a weekly public affairs television programme, it's also a finite simple group of order 898,128,000. To prevent confusion, here are a few simple ways to tell the two apart. The television programme is a flimsy and ephemeral product of human civilisation which will not long endure in this universe. The finite simple group is a logical necessity inhabiting a timeless Platonic realm of abstraction and pure truth. The television programme predicts that Pope John Paul II will win a Nobel Peace Prize. The finite simple group takes no stand on the matter. The television programme contains only very pedestrian and boring subgroups, while the finite simple group contains the Mathieu group M22 as a maximal subgroup. The television programme is generated by John McLaughlin (as far as I can tell, no relation to the jazz artist of the same name), whereas a 22-dimensional representation of the finite group over the finite field F7 is generated by the matrices

0100000000000000000000          3600000000000000000000
1000000000000000000000          0010000000000000000000
0001000000000000000000          0000100000000000000000
0010000000000000000000          0000010000000000000000
0000001000000000000000          0000000100000000000000
0000000010000000000000          0000000001000000000000
0000100000000000000000          0000000000100000000000
0000000000010000000000          4310500400000000000000
0000010000000000000000          0000000000001000000000
0000000000000100000000          0000000000000010000000
0000000000000001000000          0000000000000000100000
0000000100000000000000          0000000000000000010000
2561116463431403000000          0000000000000000001000
0000000001000000000000          0000000000000000000100
0000000000000000000010          0000000000000000000001
0000000000100000000000          3634503603202620362340
0043661213350404100000          6150405500433261654462
3416205006500132010040          5556523141121520054163
5225106102260525001050          3450340335252250144500
2543522352640541000130          2506015620240224344010
0000000000000010000000          2654224150141552331230
0052522353240445000031          0001000000000000000000.

The McLaughlin Group, and the McLaughlin group. Do not confuse the two.

Posted by aloysius at July 05, 2003 02:54 AM | TrackBack |
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