On Monomial Characters and Central Idempotents of Rational Group Algebras

2004/05/21 by Aurora Olivieri, Ángel del Río, Ángel del Rı́o +1 · 6 citations
Mathematics · #Algebraic structures and combinatorial models #Finite Group Theory Research #Advanced Algebra and Geometry

paper · doi:10.1081/agb-120028797

Abstract

Abstract 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.

Citations

• On the group ring of a finite abelian group

Cited by

• On metacyclic p-group codes
• On idempotents and the number of simple components of semisimple group algebra
• Subgroup separability in integral group rings
• Rational group algebras of finite groups: from idempotents to units of integral group rings
• Groups of units of integral group rings commensurable with direct products of free-by-free groups
• Group Algebra and Coding Theory

Related

• Primitive Central idempotents and the Wedderburn Decomposition of a Rational Abelian Group Algebra
• On idempotents and the number of simple components of semisimple group algebra
• Primitive Central Idempotents of the Group Algebra
• Rational Group Algebras of Camina p-groups
• Rational group algebras of finite groups: from idempotents to units of integral group rings