arXiv subjects
Publications and source records attributed to Mandi Schaeffer Fry.
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.
Let $G$ be a finite group and let $π$ be a set of primes. Write $\mathrm{Irr}_{π'}(G)$ for the set of irreducible characters of degree not divisible by any prime in $π$. We show that if $π$ contains at most two prime numbers and the only element in $\mathrm{Irr}_{π'}(G)$ is the principal character, then $G=1$.