Infinite alternating groups as finitary linear transformation groups

DOI10.1016/0021-8693(88)90064-6zbMath0665.20017OpenAlexW2017092545MaRDI QIDQ1115970

Jonathan I. Hall

Publication date: 1988

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(88)90064-6

zbMATH Keywords

alternating groupinfinite simple groupsclassification of finite simple groupsfinitary general linear groupperiodic subgroupfaithful projective representationfinitary linear transformationfinitary representationsinfinite simple locally finite groupsinfinite, simple, locally finite subgroup of FGL(V)sectional cover

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Subgroup theorems; subgroup growth (20E07) Periodic groups; locally finite groups (20F50) Simple groups (20E32) General theory for infinite permutation groups (20B07) Finite simple groups and their classification (20D05) Local properties of groups (20E25) Subgroups of symmetric groups (20B35)

Related Items (18)

Uniformly recurrent subgroups of simple locally finite groups ⋮ Finitary linear transformation groups and elements of finite local degree ⋮ Local characterizations of periodic simple groups of finitary transformations ⋮ Finitary linear representations of infinite symmetric and alternating groups ⋮ Locally finite simple groups of 1-type ⋮ Invariant random subgroups of inductive limits of finite alternating groups ⋮ Hall universal group as a direct limit of algebraic groups ⋮ Some countably recognizable classes of groups ⋮ The structure of groups of finitary transformations ⋮ Semiprimitivity of group algebras of locally finite groups. II ⋮ Groups of periodically defined linear transformations of an infinite-dimensional vector space ⋮ Infinite locally finite simple groups with many complemented subgroups ⋮ Finitary representations and images of transitive finitary permutation groups ⋮ Confined subgroups in periodic simple finitary linear groups ⋮ Characters of inductive limits of finite alternating groups ⋮ Irreducible periodic groups of finitary transformations ⋮ The structure of \(p\)-groups of finitary transformations ⋮ A group theoretical characterization of simple, locally finite, finitary linear groups

Cites Work

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• Existentially closed locally finite central extensions; multipliers and local systems
• The classification of the simple periodic linear groups
• Finitary linear transformation groups and elements of finite local degree
• Some groups generated by transvection subgroups
• A note on finitary permutation groups
• On the minimal degrees of projective representations of the finite Chevalley groups
• Maximal subgroups and automorphisms of Chevalley groups
• Strong finiteness conditions in locally finite groups
• On the 1-cohomology of the general and special linear groups
• The maximal subgroups of Conway's group C\(_3\) and McLaughlin's group
• Lectures on Chevalley Groups
• On the minimal dimensions of irreducible representations of symmetric groups
• MONOMORPHISMS AND DIRECT LIMITS OF FINITE GROUPS OF LIE TYPE
• Some Applications of Tree-Limits to Groups. Part 1
• Projective Representations of Minimum Degree of Group Extensions
• Subgroups of Classical Groups Generated by Long Root Elements

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