GENERALIZING A THEOREM OF HUPPERT AND MANZ

Abstract

Huppert and Manz proved that if G is a nonsolvable group where all the character degrees are square-free, then G ≅ A7 × S, where S is a solvable group with no degree divisible by 2, 3, 5, or 7. We weaken the hypothesis of Huppert and Manz's theorem to prove the following generalization. If G is a nonsolvable group and 4 divides no character degree of G, then G ≅ A7 × S, where S is a solvable group with no degree divisible by 2.