Primitive Characters and Permutation Characters of Solvable Groups

Details Primitive Characters and Permutation Characters of Solvable Groups Primitive Characters and Permutation Characters of Solvable Groups

2007-09-09

arxiv.org/abs/0709.1209v2

Mathematics

Representation Theory

Attribution given for Theorem K, which it has been pointed out to me is the odd order case of a published result of P.A. Fergu

Scientific paper

Let X be an irreducible, primitive complex character of the finite solvable group G, and let X* denote the complex conjugate character. If the degree X(1) is odd, then we show how to associate to X in a unique way, a conjugacy class of subgroups U of G for which X*X = (1_U)^G, the permutation character on the cosets of U. We investigate this situation and give a number of applications to properties of primitive characters of solvable and p-solvable groups.

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