On Monomial Characters and Central Idempotents of Rational Group Algebras

We give a method to obtain the primitive central idempotent of the rational group algebra ℚG over a finite group G associated to a monomial irreducible character which does not involve computations with the character field nor its Galois group. We also show that for abelian-by-supersolvable groups this method takes a particularly easy form that can be used to compute the Wedderburn decomposition of ℚG. Key Words: Monomial charactersPrimitive central idempotentsGroup algebrasWedderburn decomposition Acknowledgment The authors Ángel del Río and Juan Jacobo Simón are partially supported by the D.G.I. of Spain and Fundación Séneca of Murcia. Notes #Communicated by A. Turull.