On groups having a $p$-constant character
Authors:
Silvio Dolfi, Emanuele Pacifici and Lucía Sanus
Journal:
Proc. Amer. Math. Soc. 149 (2021), 107-120
MSC (2010):
Primary 20C15
DOI:
https://doi.org/10.1090/proc/15256
Published electronically:
October 20, 2020
MathSciNet review:
4172590
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Abstract | References | Similar Articles | Additional Information
Abstract: 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:
silvio.dolfi@unifi.it
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:
emanuele.pacifici@unimi.it
Lucía Sanus
Affiliation:
Departament de Matemàtiques, Facultat de Matemàtiques, Universitat de València, 46100 Burjassot, València, Spain
ORCID:
0000-0002-0258-5749
Email:
lucia.sanus@uv.es
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
Article copyright:
© Copyright 2020
American Mathematical Society
