Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



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
Published electronically: October 20, 2020
MathSciNet review: 4172590
Full-text PDF

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.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 20C15

Retrieve articles in all journals with MSC (2010): 20C15

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

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

Lucía Sanus
Affiliation: Departament de Matemàtiques, Facultat de Matemàtiques, Universitat de València, 46100 Burjassot, València, Spain
ORCID: 0000-0002-0258-5749

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