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Saturday, April 10, 2010

Geometry for Generations

Filed under: General,Geometry — m759 @ 12:25 PM

"Let G  be a finite, primitive subgroup of GL(V) = GL(n,D), where V  is an n-dimensional vector space over the division ring D.  Assume that G  is generated by 'nice' transformations.  The problem is then to try to determine (up to GL(V)-conjugacy) all possibilities for G.  Of course, this problem is very vague.  But it is a classical one, going back 150 years, and yet very much alive today."

— William M. Kantor, "Generation of Linear Groups," pp. 497-509 in The Geometric Vein: The Coxeter Festschrift, published by Springer, 1981

This quote was added today to "A Simple Reflection Group of Order 168."

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