Groups with few $p'$-character degrees

Eugenio Giannelli, Noelia Rizo, Mandi Schaeffer Fry

Published 2019-04-13Version 1

We prove a variation of Thompson's Theorem. Namely, if the first column of the character table of a finite group $G$ contains only two distinct values not divisible by a given prime number $p>3$, then $O^{pp'pp'}(G)=1$. This is done by using the classification of finite simple groups.