Characters of 𝜋’-degree

Giannelli, Eugenio; Schaeffer Fry, A.; Vallejo Rodríguez, Carolina

doi:10.1090/proc/14633

Characters of $\pi ’$-degree
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by Eugenio Giannelli, A. A. Schaeffer Fry and Carolina Vallejo Rodríguez PDF

Proc. Amer. Math. Soc. 147 (2019), 4697-4712 Request permission

Abstract:

Let $G$ be a finite group and let $\pi$ be a set of primes. Write $\operatorname {Irr}_{\pi ’}(G)$ for the set of irreducible characters of degree not divisible by any prime in $\pi$. We show that if $\pi$ contains at most two prime numbers and the only element in $\operatorname {Irr}_{\pi ’}(G)$ is the principal character, then $G=1$.

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