Abstract
A complex character of a finite group G is called orthogonal if it is the character of a real representation. If all characters of G are orthogonal, then G is called totally orthogonal. Totally orthogonal groups are generated by involutions. Necessary and sufficient conditions for total orthogonality are obtained for 2-groups, for split extensions of elementary abelian 2-groups, for Frobenius groups, and for groups whose irreducible character degrees are bounded by 2. Sylow 2-subgroups of alternating groups and finite reflection groups are observed to be totally orthogonal.
Original language | English (US) |
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Pages (from-to) | 299-310 |
Number of pages | 12 |
Journal | Journal of Pure and Applied Algebra |
Volume | 54 |
Issue number | 2-3 |
DOIs | |
State | Published - Oct 1988 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory