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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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On groups having a $p$-constant character
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by Silvio Dolfi, Emanuele Pacifici and Lucía Sanus PDF
Proc. Amer. Math. Soc. 149 (2021), 107-120 Request permission


Let $G$ be a finite group, and $p$ a prime number; a character of $G$ is called $p$-constant if it takes a constant value on all the elements of $G$ whose order is divisible by $p$. This is a generalization of the very important concept of characters of $p$-defect zero. In this paper, we characterize the finite $p$-solvable groups having a faithful irreducible character that is $p$-constant and not of $p$-defect zero, and we will show that a non-$p$-solvable group with this property is an almost-simple group.
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Additional Information
  • Silvio Dolfi
  • Affiliation: Dipartimento di Matematica e Informatica U. Dini, Università degli Studi di Firenze, viale Morgagni 67/a, 50134 Firenze, Italy
  • MR Author ID: 314262
  • ORCID: 0000-0002-0513-4249
  • Email:
  • Emanuele Pacifici
  • Affiliation: Dipartimento di Matematica F. Enriques, Università degli Studi di Milano, via Saldini 50, 20133 Milano, Italy
  • MR Author ID: 730745
  • ORCID: 0000-0001-8159-5584
  • Email:
  • Lucía Sanus
  • Affiliation: Departament de Matemàtiques, Facultat de Matemàtiques, Universitat de València, 46100 Burjassot, València, Spain
  • ORCID: 0000-0002-0258-5749
  • Email:
  • Received by editor(s): May 16, 2020
  • Received by editor(s) in revised form: June 5, 2020
  • Published electronically: October 20, 2020
  • Additional Notes: The first two authors were partially supported by the Italian INdAM-GNSAGA
    The research of the third author was partially supported by Ministerio de Ciencia e Innovación PID2019-103854GB-I00 and FEDER funds.
    The third author thanks Università degli Studi di Firenze for the financial support.

  • Dedicated: Dedicated to Carlo Casolo
  • Communicated by: Martin Liebeck
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 107-120
  • MSC (2010): Primary 20C15
  • DOI:
  • MathSciNet review: 4172590