Induced characters with equal degree constituents

Abstract

We study the situation of a finite group G having a subgroup H with the property that each of its nonprincipal irreducible (complex) characters induce to G as a sum of irreducible characters all having the same degree. When this happens, the subgroup H either contains, or is contained in, the commutator subgroup G' of G. In any case, the normal closure H-G is always proper in G whenever H is proper (even when G is perfect), and H-G is solvable whenever this normal closure is a proper subgroup of G'.