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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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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