TY - JOUR
T1 - Realizability of representations of finite groups
AU - Wang, K. S.
AU - Grove, L. C.
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 1988/10
Y1 - 1988/10
N2 - 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.
AB - 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.
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U2 - 10.1016/0022-4049(88)90036-9
DO - 10.1016/0022-4049(88)90036-9
M3 - Article
AN - SCOPUS:38249028887
VL - 54
SP - 299
EP - 310
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 2-3
ER -