Algebra & Number Theory Vol. 8, No. 2, 2014

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Groups with exactly one irreducible character of degree divisible by $p$

Daniel Goldstein, Robert M. Guralnick, Mark L. Lewis, Alexander Moretó, Gabriel Navarro and Pham Huu Tiep

Vol. 8 (2014), No. 2, 397–428

DOI: 10.2140/ant.2014.8.397

Abstract

Let $p$ be a prime. We characterize those finite groups which have precisely one irreducible character of degree divisible by $p$ .

Keywords

finite groups, characters, character degrees

Mathematical Subject Classification 2010

Primary: 20C15

Milestones

Received: 20 February 2013

Revised: 6 May 2013

Accepted: 11 July 2013

Published: 18 May 2014

Authors

Daniel Goldstein
Center for Communications Research 4320 Westerra Court San Diego, CA 92121 United States

Robert M. Guralnick
Department of Mathematics University of Southern California 3620 S. Vermont Ave. Los Angeles, CA 90089 United States

Mark L. Lewis
Department of Mathematical Sciences Kent State University Kent, OH 44242 United States

Alexander Moretó
Departament dÁlgebra, Facultat de Matemátiques Universitat de Valéncia Burjassot 46100 Valéncia Spain

Gabriel Navarro
Departament dÁlgebra, Facultat de Matemátiques Universitat de Valéncia Burjassot 46100 Valéncia Spain

Pham Huu Tiep
Department of Mathematics University of Arizona 617 N. Santa Rita Ave. P.O. Box 210089 Tucson, AZ 85721-0089 United States