A structure theorem for the unit group of the integral group ring of some finite groups

DOI10.1515/crll.2000.032zbMath0951.16011OpenAlexW2062928868WikidataQ116166415 ScholiaQ116166415MaRDI QIDQ4953851

Ángel Del Río, Eric Jespers

Publication date: 27 September 2000

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/ecbdd754d64e07234472c5db75f9fc6911e1aabc

zbMATH Keywords

finite groupssubgroups of finite indexgroups of unitsintegral group ringsmatrix rings over skew fieldssemisimple Artinian algebrasfree products of Abelian groupsunit groups of maximal orders

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Group rings (16S34) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Units, groups of units (associative rings and algebras) (16U60)

Related Items (12)

On Monomial Characters and Central Idempotents of Rational Group Algebras ⋮ Primitive Central Idempotents in Rational Group Algebras ⋮ COMPUTING LARGE DIRECT PRODUCTS OF FREE GROUPS IN INTEGRAL GROUP RINGS ⋮ Unnamed Item ⋮ A dichotomy for integral group rings via higher modular groups as amalgamated products ⋮ Groups of units of integral group rings commensurable with direct products of free-by-free groups. ⋮ Bass units as free factors in integral group rings of simple groups. ⋮ An algorithm to compute the primitive central idempotents and the Wedderburn decomposition of a rational group algebra. ⋮ Abelianization and fixed point properties of units in integral group rings ⋮ Subgroup separability in integral group rings. ⋮ Group algebras of Kleinian type and groups of units. ⋮ Computing the Wedderburn decomposition of group algebras by the Brauer–Witt theorem

Cites Work

• Degree 1 and 2 representations of nilpotent groups and applications to units of group rings
• Free products of abelian groups in the unit group of integral group rings
• Unnamed Item

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