## 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 $G=1$.## References

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## Additional Information

**Eugenio Giannelli**- Affiliation: Dipartimento di Matematica e Informatica, U. Dini, V. Morgagni 67, Firenze, Italy
- MR Author ID: 1011546
- Email: eugenio.giannelli@unifi.it
**A. A. Schaeffer Fry**- Affiliation: Department of Mathematical and Computer Sciences, Metropolitan State University of Denver, Denver, Colorado 80217
- MR Author ID: 899206
- Email: aschaef6@msudenver.edu
**Carolina Vallejo Rodríguez**- Affiliation: ICMAT, Campus Cantoblanco UAM, C/ Nicolás Cabrera, 13-15, 28049 Madrid, Spain
- MR Author ID: 1001337
- ORCID: 0000-0003-3363-3376
- Email: carolina.vallejo@icmat.es
- Received by editor(s): October 2, 2018
- Received by editor(s) in revised form: February 26, 2019
- Published electronically: June 10, 2019
- Additional Notes: The second-named author was partially supported by a grant from the National Science Foundation (Award No. DMS-1801156)

The third-named author was partially supported by the Spanish Ministerio de Educación y Ciencia Proyectos MTM2016-76196-P and the ICMAT Severo Ochoa project SEV-2011-0087 - Communicated by: Pham Huu Tiep
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 4697-4712 - MSC (2010): Primary 20C15, 20C30, 20C33
- DOI: https://doi.org/10.1090/proc/14633
- MathSciNet review: 4011506