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10/28/2014 - 12:15pm

10/28/2014 - 1:10pm

Speaker:

Will Murray (California State University Long Beach)

Abstract:

Question: Given a field, what interesting finite multiplicative groups does it contain?

Answer: None. In algebra class we prove that any finite group in a field is cyclic.

However, division rings (noncommutative fields) are much more interesting. At the very least, we know that the quaternions contain the finite quaternion group {1,-1,i,-i,j,-j,k,-k}, which is not cyclic. Lots of interesting geometry gives us a classification of all finite subgroups of the quaternions. They correspond to subgroups of SU(2) and SO(3), which correspond in turn to rotation groups of the Platonic solids.

Where:

MDSL 126