Characters of groups having fixed-point-free automorphisms of 2-power order

Let C be a cyclic 2-group that acts fixed-point-freely on a group K, and let T⊆C be the subgroup of index 2. The main result of this paper is that the square-free parts of the degrees of the T-invariant irreducible characters of K are never divisible by primes p≡−1 mod |C|.