Unit Groups of Integral Finite Group Rings with No Noncyclic Abelian Finitep-Subgroups

DOI10.1080/00927870802103669zbMath1156.16023arXiv0704.0412OpenAlexW2964335316MaRDI QIDQ3529051

Martin Hertweck

Publication date: 20 October 2008

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

Full work available at URL: https://arxiv.org/abs/0704.0412

zbMATH Keywords

finite groupsintegral group ringsgroups of normalized unitspartial augmentationstorsion units

Mathematics Subject Classification ID

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

Related Items (9)

Sylow like theorems for $V(mathbb{Z}G)$ ⋮ Algorithmic Aspects of Units in Group Rings ⋮ A Sylow theorem for the integral group ring of \(\mathrm{PSL}(2,q)\) ⋮ 𝑝-subgroups of units in ℤ𝔾 ⋮ On torsion subgroups in integral group rings of finite groups. ⋮ Subgroup isomorphism problem for units of integral group rings ⋮ From examples to methods: Two cases from the study of units in integral group rings ⋮ Finite groups of units and their composition factors in the integral group rings of the groups PSL(2, q) ⋮ Torsion subgroups in the units of the integral group ring of \(\mathrm{PSL}(2,p^3)\).

Cites Work

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• Rigidity of \(p\)-adic \(p\)-torsion
• Units of integral group rings of metabelian groups
• Finite Subgroups in Integral Group Rings
• ON FINITE GROUPS OF EVEN ORDER WHOSE 2-SYLOW GROUP IS A QUATERNION GROUP
• UNITS IN INTEGRAL METABELIAN GROUPRINGS I, JACKSON'S UNIT THEOREM REVISITED
• Reduction theory in algebraic number fields
• The unit group of 1+Δ(G)Δ(A) is torsion-free
• On the Structure of Group Algebras, I
• The Units of Group-Rings

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