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Characters of $ \pi'$-degree


Authors: Eugenio Giannelli, A. A. Schaeffer Fry and Carolina Vallejo Rodríguez
Journal: Proc. Amer. Math. Soc. 147 (2019), 4697-4712
MSC (2010): Primary 20C15, 20C30, 20C33
DOI: https://doi.org/10.1090/proc/14633
Published electronically: June 10, 2019
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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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Additional Information

Eugenio Giannelli
Affiliation: Dipartimento di Matematica e Informatica, U. Dini, V. Morgagni 67, Firenze, Italy
Email: eugenio.giannelli@unifi.it

A. A. Schaeffer Fry
Affiliation: Department of Mathematical and Computer Sciences, Metropolitan State University of Denver, Denver, Colorado 80217
Email: aschaef6@msudenver.edu

Carolina Vallejo Rodríguez
Affiliation: ICMAT, Campus Cantoblanco UAM, C/ Nicolás Cabrera, 13-15, 28049 Madrid, Spain
Email: carolina.vallejo@icmat.es

DOI: https://doi.org/10.1090/proc/14633
Keywords: Character degrees, perfect groups
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
Article copyright: © Copyright 2019 American Mathematical Society