Further Developments
Clifford's theorem has led to a branch of representation theory in its own right, now known as Clifford theory. This is particularly relevant to the representation theory of finite solvable groups, where normal subgroups usually abound. For more general finite groups, Clifford theory often allows representation-theoretic questions to be reduced to questions about groups which are close (in a sense which can be made precise) to being simple.
Mackey (1976) found a more precise version of this result for the restriction of irreducible unitary representations of locally compact groups to closed normal subgroups in what has become known as the "Mackey machine" or "Mackey normal subgroup analysis".
Read more about this topic: Clifford Theory
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