Finite groups of units and their composition factors in the integral group rings of the groups PSL(2, q)

DOI10.1515/JGT.2009.019zbMath1191.16036arXiv0810.0186OpenAlexW2963602331MaRDI QIDQ3401160

Martin Hertweck, Wolfgang Kimmerle, Christian R. Höfert

Publication date: 29 January 2010

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.0186

zbMATH Keywords

finite subgroupsrepresentationsgroups of unitssimple groupsintegral group ringslinear groupstorsion unitsZassenhaus conjecture

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 (13)

Torsion units for a Ree group, Tits group and a Steinberg triality group. ⋮ Sylow like theorems for $V(mathbb{Z}G)$ ⋮ Algorithmic Aspects of Units in Group Rings ⋮ A Sylow theorem for the integral group ring of \(\mathrm{PSL}(2,q)\) ⋮ On torsion subgroups in integral group rings of finite groups. ⋮ On the prime graph question for integral group rings of 4-primary groups. II. ⋮ Subgroup isomorphism problem for units of integral group rings ⋮ Torsion units for some almost simple groups ⋮ ZASSENHAUS CONJECTURE FOR INTEGRAL GROUP RING OF SIMPLE LINEAR GROUPS ⋮ Torsion units in the integral group ring of PSL(3, 4) ⋮ On the determination of Sylow numbers ⋮ From examples to methods: Two cases from the study of units in integral group rings ⋮ Torsion subgroups in the units of the integral group ring of \(\mathrm{PSL}(2,p^3)\).

Cites Work

• Autoequivalences of blocks and a conjecture of Zassenhaus
• The characterization of finite groups with abelian Sylow 2-subgroups
• The characterization of finite groups with dihedral Sylow 2-subgroups. I, II
• On groups with abelian Sylow 2-subgroups
• On the maximal subgroups of finite simple group
• TORSION UNITS IN INTEGRAL GROUP RINGS OF CERTAIN METABELIAN GROUPS
• Unit Groups of Integral Finite Group Rings with No Noncyclic Abelian Finitep-Subgroups
• The Orders of Torsion Units in Integral Group Rings of Finite Solvable Groups
• Composition Factors from the Group Ring and Artin's Theorem on Orders of Simple Groups
• Torsion units in integral group rings.
• Integral group rings of frobenius groups and the conjectures of H.J. Zassenhaus
• Simple Components of Q[SL(2,q)]
• On the Structure of Group Algebras, I
• Nonsolvable finite groups all of whose local subgroups are solvable

This page was built for publication: Finite groups of units and their composition factors in the integral group rings of the groups PSL(2, q)