#### Vol. 7, No. 3, 2013

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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
Primary: 20C15
Secondary: 20C33