On the degrees of irreducible characters fixed by some field automorphism

Nicola Grittini

Published 2020-11-07Version 1

It is known that, if all the irreducible real valued characters of a finite group are of odd degree, then the group has a normal Sylow 2-subgroup. In this paper, we prove and analogous result for solvable groups, by taking into account the degree of irreducible characters fixed by some field isomorphism of prime order $p$. We prove it as a consequence of a more general result.