Log24

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

 

No Comments

No comments yet.

RSS feed for comments on this post.

Sorry, the comment form is closed at this time.

Powered by WordPress