Computing generators of the unit group of an integral Abelian group ring.

DOI10.1016/j.jalgebra.2012.09.031zbMath1271.16038arXiv1301.1770OpenAlexW2963032879MaRDI QIDQ2377446

Paolo Faccin, Willem A. De Graaf, Wilhelm Plesken

Publication date: 2 July 2013

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

Full work available at URL: https://arxiv.org/abs/1301.1770

zbMATH Keywords

algorithmsalgebraic groupsfinite Abelian groupsintegral group ringsarithmetic groupsgenerators of unit groupsHoechsmann units

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Group rings (16S34) Generators, relations, and presentations of groups (20F05) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Computational aspects of associative rings (general theory) (16Z05) Units, groups of units (associative rings and algebras) (16U60)

Related Items (6)

Equivalence of Lattice Orbit Polytopes ⋮ Integrality and arithmeticity of solvable linear groups. ⋮ The isomorphism problem for torsion free nilpotent groups of Hirsch length at most \(5\) ⋮ Units on the Gauss extension of a Galois ring ⋮ Linear groups and computation ⋮ COMPUTING NORMAL INTEGRAL BASES OF ABELIAN NUMBER FIELDS

Uses Software

• Magma

Cites Work

• Decompositions of algebras over \(\mathbb{R}\) and \(\mathbb{C}\)
• Decomposition of algebras over finite fields and number fields
• Constructing units in commutative group rings
• The Magma algebra system. I: The user language
• Computing residue class rings and Picard groups of orders
• New techniques for computing the ideal class group and a system of fundamental units in number fields
• Computing the multiplicative group of residue class rings
• On the group ring of a finite abelian group
• The Units of Group-Rings
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