So last time we proved that the dimensions of an irreducible representation divide the index of the center. Now to generalize this to an arbitrary abelian normal subgroup.

There are first a few basic background results that I need to talk about.

**Induction **

Given a group and a subgroup (in fact, this can be generalized to a non-monomorphic map ), a representation of yields by **restriction** a representation of . One obtains a functor . This functor has an adjoint, denoted by . (more…)