Construction of central units in integral group rings of finite groups

DOI10.1090/S0002-9939-2011-10968-7zbMath1246.16028OpenAlexW2094960014MaRDI QIDQ5388788

Eric Jespers, Michael M. Parmenter

Publication date: 20 April 2012

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2011-10968-7

zbMATH Keywords

finite groupssubgroups of finite indexgroups of unitsmonomial groupsintegral group ringsprimitive central idempotentsrational group algebrascentral units

Mathematics Subject Classification ID

Group rings (16S34) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Center, normalizer (invariant elements) (associative rings and algebras) (16U70) Units, groups of units (associative rings and algebras) (16U60)

Related Items (5)

On idempotents and the number of simple components of semisimple group algebras ⋮ A generalization of strongly monomial groups ⋮ Integral group rings with all central units trivial ⋮ Central units of integral group rings ⋮ On the index of a free abelian subgroup in the group of central units of an integral group ring.

Cites Work

• Unnamed Item
• Units of group rings of solvable and Frobenius groups over large rings of cyclotomic integers
• The Dirichlet unit theorem, induced characters, and Whitehead groups of finite groups
• On Monomial Characters and Central Idempotents of Rational Group Algebras
• Computing the Wedderburn decomposition of group algebras by the Brauer–Witt theorem
• Central Units in Metacyclic Integral Group Rings
• Central Idempotents and Units in Rational Group Algebras of Alternating Groups
• Central units of integral group rings of nilpotent groups
• Central units of the integral group ring $\mathbb {Z}A_5$

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