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.
Original language | English (US) |
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Pages (from-to) | 567-593 |
Number of pages | 27 |
Journal | Algebra and Number Theory |
Volume | 7 |
Issue number | 3 |
DOIs | |
State | Published - 2013 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
Keywords
- Frobenius-Schur indicator
- Nonvanishing element
- Real irreducible character