Sur l'Indice de Schur Dans les Groupes Dont les Caracteres Sont a Valeurs Rationnelles

Ion Armeanu

Publications de l'Institut Mathématique, _N_S_54 (1993) no. 68, p. 29 .

Résumé

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 $G$.

Détail

Classification : 20C15