Realizability of representations of finite groups

K. S. Wang, L. C. Grove

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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 languageEnglish (US)
Pages (from-to)299-310
Number of pages12
JournalJournal of Pure and Applied Algebra
Volume54
Issue number2-3
DOIs
StatePublished - Oct 1988

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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