On the prime graph question for integral group rings of Conway simple groups

DOI10.1016/j.jsc.2019.02.005zbMath1425.16018arXiv1711.11322OpenAlexW2964185361MaRDI QIDQ2000268

Leo Margolis

Publication date: 28 June 2019

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

Full work available at URL: https://arxiv.org/abs/1711.11322

zbMATH Keywords

sporadic simple groupsunit groupgroup ringprime graph question

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Group rings (16S34) 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)

Related Items (3)

From examples to methods: Two cases from the study of units in integral group rings ⋮ An application of blocks to torsion units in group rings ⋮ Orders of units in integral group rings and blocks of defect 1

Uses Software

• GAP
• GAP Character Table Library
• CTblLib
• AtlasRep
• Help

Cites Work

• Group ring groups. Volume 1: Orders and generic constructions of units.
• Integral group ring of the Mathieu simple group \(M_{12}\).
• Zassenhaus conjecture for \(A_5\)
• HeLP: a GAP package for torsion units in integral group rings
• A counterexample to the first Zassenhaus conjecture
• Recent advances on torsion subgroups of integral group rings
• TORSION UNITS IN INTEGRAL GROUP RINGS OF CONWAY SIMPLE GROUPS
• Integral group ring of Rudvalis simple group
• Torsion units in integral group ring of Higman-Sims simple group
• Torsion units in integral group rings of Janko simple groups
• 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
• Integral group ring of the Suzuki sporadic simple group
• Integral group ring of the McLaughlin simple group
• 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
• On the prime graph question for almost simple groups with an alternating socle
• On the Structure of Group Algebras, I
• INTEGRAL GROUP RING OF THE MATHIEU SIMPLE GROUP M₂₄
• A counterexample to the isomorphism problem for integral group rings
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