From examples to methods: Two cases from the study of units in integral group rings

DOI10.1007/s13226-021-00180-yzbMath1497.16036arXiv2006.09031OpenAlexW3209977258MaRDI QIDQ2065332

Andreas Bächle, Leo Margolis

Publication date: 7 January 2022

Published in: Indian Journal of Pure \& Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.09031

zbMATH Keywords

unit groupZassenhaus conjectureintegral group ringprime graph question

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Modular representations and characters (20C20) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Units, groups of units (associative rings and algebras) (16U60)

Uses Software

• GAP
• Normaliz
• 4ti2
• Help

Cites Work

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• Subgroup isomorphism problem for units of integral group rings
• Torsion units of integral group rings of metacyclic groups
• Group ring groups. Volume 1: Orders and generic constructions of units.
• Group ring groups. Volume 2: Structure theorems of unit groups.
• The power of pyramid decomposition in Normaliz
• Zassenhaus conjecture for \(A_6\).
• Mini-workshop: Arithmetic of group rings. Abstracts from the mini-workshop held November 25 -- December 1, 2007.
• Torsion units in integral group rings of some metabelian groups. II
• Zassenhaus conjecture for \(A_5\)
• A characterization of units in \(\mathbb{Z} [A_4\)]
• An introduction to group rings
• On the prime graph question for integral group rings of 4-primary groups. II.
• HeLP: a GAP package for torsion units in integral group rings
• A counterexample to the first Zassenhaus conjecture
• On the prime graph question for integral group rings of Conway simple groups
• Zassenhaus conjecture on torsion units holds for \(\text{SL}(2, {p})\) and \(\text{SL}(2, {p}^2)\)
• Revisiting the Zassenhaus conjecture on torsion units for the integral group rings of small groups.
• Torsion subgroups in the units of the integral group ring of \(\mathrm{PSL}(2,p^3)\).
• Zassenhaus conjecture on torsion units holds for \(\mathrm{PSL}(2,p)\) with \(p\) a Fermat or Mersenne prime
• Partial augmentations power property: a Zassenhaus conjecture related problem
• On torsion subgroups in integral group rings of finite groups.
• Zassenhaus Conjecture for cyclic-by-abelian groups
• Torsion units in integral group rings of Janko simple groups
• Torsion Units in Integral Group Ring of the Mathieu Simple GroupM₂₂
• The Group of Units of the Integral Group Ring ZS₃
• Zassenhaus conjecture for S₅
• Finite groups of units and their composition factors in the integral group rings of the groups PSL(2, q)
• TORSION UNITS IN INTEGRAL GROUP RINGS OF CERTAIN METABELIAN GROUPS
• Unit Groups of Integral Finite Group Rings with No Noncyclic Abelian Finitep-Subgroups
• Torsion units in integral group rings.
• Units of integral group rings of Frobenius groups
• Rational Conjugacy of Torsion Units in Integral Group Rings of Non-Solvable Groups
• On the Gruenberg–Kegel graph of integral group rings of finite groups
• On the prime graph question for integral group rings of 4-primary groups I
• The Status of the Zassenhaus Conjecture for Small Groups
• ZASSENHAUS CONJECTURE FOR INTEGRAL GROUP RING OF SIMPLE LINEAR GROUPS
• Orders of units in integral group rings and blocks of defect 1
• On the First Zassenhaus Conjecture and Direct Products
• Finite Subgroups of Group Rings: A survey
• An application of blocks to torsion units in group rings
• On the prime graph question for almost simple groups with an alternating socle
• On the Torsion Units of Some Integral Group Rings
• On the Structure of Group Algebras, I
• 𝑝-subgroups of units in ℤ𝔾
• Torsion Units in the Integral Group Ring of the Alternating Group of Degree 6
• Indecomposable representations of finite groups over the ring of 𝑝-adic integers
• The Units of Group-Rings
• A counterexample to the isomorphism problem for integral group rings

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