Torsion units in integral group rings of Janko simple groups

DOI10.1090/S0025-5718-2010-02376-2zbMath1209.16026arXivmath/0608441OpenAlexW1976524169MaRDI QIDQ3081300

Victor A. Bovdi, Eric Jespers, Olexandr Konovalov

Publication date: 7 March 2011

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0608441

zbMATH Keywords

integral group ringsprime graphsKimmerle conjecturepartial augmentationstorsion unitsZassenhaus conjecturenormalized unit groupsJanko sporadic simple groups

Mathematics Subject Classification ID

Simple groups: sporadic groups (20D08) 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 (14)

Torsion units for a Ree group, Tits group and a Steinberg triality group. ⋮ Sylow like theorems for $V(mathbb{Z}G)$ ⋮ Group algebras. ⋮ 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 ⋮ On torsion subgroups in integral group rings of finite groups. ⋮ INTEGRAL GROUP RING OF THE MATHIEU SIMPLE GROUP M₂₄ ⋮ TORSION UNITS IN INTEGRAL GROUP RINGS OF CONWAY SIMPLE GROUPS ⋮ On the prime graph question for integral group rings of Conway simple groups ⋮ Torsion units for some almost simple groups ⋮ ZASSENHAUS CONJECTURE FOR INTEGRAL GROUP RING OF SIMPLE LINEAR GROUPS ⋮ Torsion units for some projected special linear groups ⋮ Torsion units in the integral group ring of PSL(3, 4) ⋮ From examples to methods: Two cases from the study of units in integral group rings

Uses Software

• GAP
• LAGUNA
• MINION

Cites Work

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• Integral group ring of the Mathieu simple group \(M_{12}\).
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• Zassenhaus conjecture for \(A_5\)
• Torsion Units in Integral Group Ring of the Mathieu Simple GroupM₂₂
• Kimmerle conjecture for the Held and O'Nan sporadic simple groups
• Integral Group Ring of the Mathieu Simple GroupM₂₃
• TORSION UNITS IN INTEGRAL GROUP RINGS OF CERTAIN METABELIAN GROUPS
• Integral group ring of the Suzuki sporadic simple group
• The Orders of Torsion Units in Integral Group Rings of Finite Solvable Groups
• Integral group ring of the McLaughlin simple group
• On the Torsion Units of Some Integral Group Rings
• On the Structure of Group Algebras, I
• Zassenhaus conjecture for central extensions of S 5

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