Centralizers of Elements in Locally Finite Simple Groups

DOI10.1112/plms/s3-62.2.301zbMath0682.20020OpenAlexW2087377863MaRDI QIDQ4731361

Brian Hartley, Mahmut Kuzucuoǧlu

Publication date: 1991

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/plms/s3-62.2.301

zbMATH Keywords

centralizersDynkin diagramsChevalley groupsunipotent elementsclassification of finite simple groupssemisimple elementsextended Dynkin diagramconnected reductive algebraic groupsimply connected simple algebraic grouplocally finite simple groupsinfinite locally finite fieldsfundamental rootslocally finite simple linear group

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Subgroup theorems; subgroup growth (20E07) Periodic groups; locally finite groups (20F50) Simple groups (20E32) Finite simple groups and their classification (20D05) Local properties of groups (20E25)

Related Items (19)

Centralizers of semisimple subgroups in locally finite simple groups ⋮ On supersimple groups ⋮ Elements of specified order in simple algebraic groups ⋮ Centralisers of finite groups in locally finite simple groups ⋮ Automorphism Orbits and Element Orders in Finite Groups: Almost-Solubility and the Monster ⋮ Barely transitive permutation groups ⋮ Centralizers of abelian subgroups in locally finite simple groups ⋮ Centralizers of involutions in locally finite-simple groups. ⋮ Finite groups with a large automorphism orbit ⋮ On simple periodic linear groups -- dense subgroups, permutation representations, and induced modules ⋮ Locally finite groups and their subgroups with small centralizers ⋮ Aspects of the conjugacy class structure of simple algebraic groups. ⋮ Centralizers of Involutions in Locally Finite Groups ⋮ Non-simplicity of locally finite barely transitive groups ⋮ CENTRALIZERS OF p-SUBGROUPS IN SIMPLE LOCALLY FINITE GROUPS ⋮ Locally Finite Groups with Centralizers of Finite Rank ⋮ On centralizers of locally finite simple groups ⋮ Centralizers of Finite p-Subgroups in Simple Locally Finite Groups ⋮ Centralizers of Subgroups in Direct Limits of Symmetric Groups with Strictly Diagonal Embedding

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