Representation Theory
The irreducible complex representations of a Frobenius group G can be read off from those of H and K. There are two types of irreducible representations of G:
- Any irreducible representation R of H gives an irreducible representation of G using the quotient map from G to H (that is, as a restricted representation). These give the irreducible representations of G with K in their kernel.
- If S is any non-trivial irreducible representation of K, then the corresponding induced representation of G is also irreducible. These give the irreducible representations of G with K not in their kernel.
Read more about this topic: Frobenius Group
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“Don’t confuse hypothesis and theory. The former is a possible explanation; the latter, the correct one. The establishment of theory is the very purpose of science.”
—Martin H. Fischer (1879–1962)