Some solvable character degree sets

Abstract

ABSTRACTA set of positive integers Ω containing 1 is called a solvable character degree set if all groups G satisfying cd(G) = Ω are solvable groups, where cd(G) is the set of all irreducible character degrees of G. In this paper, we find solvable character degree subsets of the set Ω = {1,a,b,c,d,ac,ad,bc,bd}, where a,b,c, and d are pairwise relatively prime integers, and we show a character degree subset Φ⊆Ω is a solvable character degree set if for all f≥2.