Invariant characters and coprime actions on finite nilpotent groups

Abstract.

Suppose that a group A acts via automorphisms on a nilpotent group G having coprime order. Given an A-invariant character $\chi \in {\rm Irr}(G)$, we show that the A-primitive irreducible characters that induce $\chi$ from an A-invariant subgroup of G all have equal degree. We use this result to obtain some information about the characters of groups of p-length 1.