Groups with an Irreducible Character of Large Degree are Solvable

Frank DeMeyer
1970 Proceedings of the American Mathematical Society  
The degree of an irreducible complex character afforded by a finite group is bounded above by the index of an abelian normal subgroup and by the square root of the index of the center. Whenever a finite group affords an irreducible character whose degree achieves these two upper bounds the group must be solvable. Let G be a finite group with an irreducible (complex) character f.
doi:10.2307/2036654 fatcat:22vxmi666zfyja4lmfasff5soe