On Monomial Characters and Central Idempotents of Rational Group Algebras

DOI10.1081/AGB-120028797zbMath1081.20001MaRDI QIDQ3154528

Ángel Del Río, Juan Jacobo Simón, Aurora A. Olivieri

Publication date: 14 January 2005

Published in: Communications in Algebra (Search for Journal in Brave)

zbMATH Keywords

group ringsprimitive central idempotentsrational group algebrasmonomial characters

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Group rings (16S34) Group rings of finite groups and their modules (group-theoretic aspects) (20C05)

Related Items (42)

Primitive Central Idempotents in Rational Group Algebras ⋮ On matrix units of semisimple group algebras ⋮ On the embedding of finite solvable groups ⋮ On idempotents and the number of simple components of semisimple group algebras ⋮ Ring isomorphism of cyclic cyclotomic algebras. ⋮ A generalization of strongly monomial groups ⋮ Wedderburn decomposition of finite group algebras. ⋮ Group algebras and coding theory ⋮ Character triples and Shoda pairs ⋮ Nilpotent decomposition in integral group rings ⋮ Groups of units of integral group rings commensurable with direct products of free-by-free groups. ⋮ Central units of integral group rings of monomial groups ⋮ Semisimple metacyclic group algebras. ⋮ Integral group rings with all central units trivial ⋮ An algorithm to compute the primitive central idempotents and the Wedderburn decomposition of a rational group algebra. ⋮ On the congruence subgroup problem for integral group rings ⋮ Character degrees of finite \(p\)-groups by coclass. ⋮ Aritmethic lattices of \(\operatorname{SO}(1,n)\) and units of group rings ⋮ Subgroup separability in integral group rings. ⋮ Coherent groups of units of integral group rings and direct products of free groups ⋮ Finite group algebras of nilpotent groups: a complete set of orthogonal primitive idempotents. ⋮ A computational approach to Brauer Witt theorem using Shoda pair theory ⋮ Group rings of finite strongly monomial groups: central units and primitive idempotents. ⋮ Rational group algebras of finite groups: from idempotents to units of integral group rings. ⋮ On idempotents of a class of commutative rings ⋮ Primitive idempotents of Schur rings. ⋮ Construction of central units in integral group rings of finite groups ⋮ Finite semisimple group algebra of a normally monomial group ⋮ Structure of finite dihedral group algebra. ⋮ PRIMITIVE CENTRAL IDEMPOTENTS OF RATIONAL GROUP ALGEBRAS ⋮ Group algebras of Kleinian type and groups of units. ⋮ THE RATIONAL GROUP ALGEBRA OF A FINITE GROUP ⋮ Central units of integral group rings ⋮ Describing units of integral group rings up to commensurability. ⋮ Semisimple finite group algebra of a generalized strongly monomial group ⋮ Extremely strong Shoda pairs with \texttt{GAP}. ⋮ An algorithm to compute the Wedderburn decomposition of semisimple group algebras implemented in the GAP package \texttt{wedderga}. ⋮ Connecting monomiality questions with the structure of rational group algebras ⋮ Computing the Wedderburn decomposition of group algebras by the Brauer–Witt theorem ⋮ The Algebraic Structure of Finite Metabelian Group Algebras ⋮ On the index of a free abelian subgroup in the group of central units of an integral group ring. ⋮ Construction of minimal non-abelian left group codes

Cites Work

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• Generators of large subgroups of the unit group of integral group rings
• An algorithm to compute the primitive central idempotents and the Wedderburn decomposition of a rational group algebra.
• Construction of Units in Integral Group Rings of Finite Nilpotent Groups
• Units of Integral Group Rings of Some Metacyclic Groups
• On the automorphism groups of rational group algebras of metacyclic groups
• CENTRAL IDEMPOTENTS IN THE RATIONAL GROUP ALGEBRA OF A FINITE NILPOTENT GROUP
• COMPUTING LARGE DIRECT PRODUCTS OF FREE GROUPS IN INTEGRAL GROUP RINGS
• A structure theorem for the unit group of the integral group ring of some finite groups
• On the group ring of a finite abelian group
• The Schur subgroup of the Brauer group

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