Sur l'Indice de Schur Dans les Groupes Dont les Caracteres Sont a Valeurs Rationnelles
Publications de l'Institut Mathématique, _N_S_54 (1993) no. 68, p. 29
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
We prove that if $G$ is a solvable group with rational
characters and {\bf R} is a splitting field for $G$, then
{\bf Q}$(2^{1/2})$ is also a splitting field for $G$ and we obtain
some sufficient conditions which guarantee that an irréductible
character $\Gamma$ of a group with rational characters has Schur
indices $m_Q(\Gamma)=1$. These results are related to the Gow
conjecture [2] wich asserts that for a solvable group whose
characters are rational valued and {\bf R} is a splitting field for
$G$, then {\bf Q} is also a splitting field for $G$.
Classification :
20C15
Ion Armeanu. Sur l'Indice de Schur Dans les Groupes Dont les Caracteres Sont a Valeurs Rationnelles. Publications de l'Institut Mathématique, _N_S_54 (1993) no. 68, p. 29 . http://geodesic.mathdoc.fr/item/PIM_1993_N_S_54_68_a4/
@article{PIM_1993_N_S_54_68_a4,
author = {Ion Armeanu},
title = {Sur {l'Indice} de {Schur} {Dans} les {Groupes} {Dont} les {Caracteres} {Sont} a {Valeurs} {Rationnelles}},
journal = {Publications de l'Institut Math\'ematique},
pages = {29 },
year = {1993},
volume = {_N_S_54},
number = {68},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1993_N_S_54_68_a4/}
}
TY - JOUR AU - Ion Armeanu TI - Sur l'Indice de Schur Dans les Groupes Dont les Caracteres Sont a Valeurs Rationnelles JO - Publications de l'Institut Mathématique PY - 1993 SP - 29 VL - _N_S_54 IS - 68 UR - http://geodesic.mathdoc.fr/item/PIM_1993_N_S_54_68_a4/ LA - en ID - PIM_1993_N_S_54_68_a4 ER -