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Thursday, August 4, 2005

Thursday August 4, 2005

Filed under: General,Geometry — Tags: — m759 @ 1:00 PM
Visible Mathematics, continued

Today’s mathematical birthdays:
Saunders Mac Lane, John Venn,
and Sir William Rowan Hamilton.

It is well known that the quaternion group is a subgroup of GL(2,3), the general linear group on the 2-space over GF(3), the 3-element Galois field.

The figures below illustrate this fact.

The image “http://www.log24.com/theory/images/Quaternions2.jpg” cannot be displayed, because it contains errors.

Related material: Visualizing GL(2,p)

“The typical example of a finite group is GL(n,q), the general linear group of n dimensions over the field with q elements. The student who is introduced to the subject with other examples is being completely misled.”

 — J. L. Alperin, book review,
    Bulletin (New Series) of the American
    Mathematical Society 10 (1984), 121

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