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Divisibility theorems for group representations October 11, 2009

Posted by Akhil Mathew in algebra, representation theory.
Tags: , , ,

There are many elegant results on the dimensions of the simple representations of a finite group {G}, of which I would like to discuss a few today.

The final, ultimateĀ goal is:

Theorem 1 Let {G} be a finite group and {A} an abelian normal subgroup. Then each simple representation of {G} has dimension dividing {|G|/|A|}. (more…)