Vol. 7, No. 3, 2013

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Zeros of real irreducible characters of finite groups

Selena Marinelli and Pham Huu Tiep

Vol. 7 (2013), No. 3, 567–593
Abstract

We prove that if all real-valued irreducible characters of a finite group G with Frobenius–Schur indicator 1 are nonzero at all 2-elements of G, then G has a normal Sylow 2-subgroup. This result generalizes the celebrated Ito–Michler theorem (for the prime 2 and real, absolutely irreducible, representations), as well as several recent results on nonvanishing elements of finite groups.

Keywords
real irreducible character, nonvanishing element, Frobenius–Schur indicator
Mathematical Subject Classification 2010
Primary: 20C15
Secondary: 20C33
Milestones
Received: 21 March 2011
Revised: 2 February 2012
Accepted: 16 March 2012
Published: 23 August 2013
Authors
Selena Marinelli
Dipartimento di Matematica L. Tonelli
Università di Pisa
Largo Bruno Pontecorvo 5
I-56127 Pisa
Italy
Pham Huu Tiep
Department of Mathematics
University of Arizona
617 N. Santa Rita Ave.
P.O. Box 210089
Tucson AZ 85721-0089
United States
http://math.arizona.edu/~tiep/