On simple periodic linear groups -- dense subgroups, permutation representations, and induced modules

DOI10.1007/BF02808115zbMath0805.20037MaRDI QIDQ689856

Brian Hartley, Alexander E. Zalesskij

Publication date: 8 February 1995

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

zbMATH Keywords

maximal subgroupsgroup ringssimple algebraic groupChevalley groupsdense subgrouppermutation representationregular orbitZariski-dense subgroupspermutation modulealgebraic extensions of finite fieldssimple locally finite groups

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Subgroup theorems; subgroup growth (20E07) Maximal subgroups (20E28) Periodic groups; locally finite groups (20F50) Simple groups (20E32) Representation theory for linear algebraic groups (20G05) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07)

Related Items (8)

Uniformly recurrent subgroups of simple locally finite groups ⋮ Positive definite functions of finitary isometry groups over fields of odd characteristic. ⋮ A family of exotic group C*-algebras ⋮ Invariant ideals of abelian group algebras and representations of groups of Lie type ⋮ A note on the conjugacy problem for finite Sylow subgroups of linear pseudofinite groups ⋮ Confined subgroups in periodic simple finitary linear groups ⋮ Some results concerning simple locally finite groups of 1-type. ⋮ Quasi-regular representations of discrete groups and associated $C^*$-algebras

Cites Work

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• Homomorphismes abstraits de groupes algébriques simples
• The classification of the simple periodic linear groups
• Character value estimates for groups of Lie type
• Fixed Points of Automorphisms of Certain Locally Finite Groups and Chevalley Groups
• The maximal subgroups of classical algebraic groups
• PERIODIC LOCALLY SOLUBLE GROUPS CONTAINING AN ELEMENT OF PRIME ORDER WITH ČERNIKOV CENTRALIZER
• Maximal subgroups of exceptional algebraic groups
• Group Rings with Simple Augmentation Ideals
• Centralizers of Elements in Locally Finite Simple Groups
• Endomorphisms of linear algebraic groups

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