Originally posted on Delta Epsilons:

There are many elegant results on the dimensions of the simple representations of a finite group $latex {G}&fg=000000$, of which I would like to discuss a few today.

The final, ultimate goal is:

Theorem 1Let $latex {G}&fg=000000$ be a finite group and $latex {A}&fg=000000$ an abelian normal subgroup. Then each simple representation of $latex {G}&fg=000000$ has dimension dividing $latex {|G|/|A|}&fg=000000$.

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