The structure of groups of finitary transformations

DOI10.1016/0021-8693(88)90068-3zbMath0669.20031OpenAlexW2001975835MaRDI QIDQ1118691

Richard E. Phillips

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)90068-3

zbMATH Keywords

vector spacefinitary linear groupsactionhomogeneous componentspermutation actionpermutation modulefull group of invertible linear transformationsgroup of finitary permutationsinfinite simple locally finite k-finitary linear groupinvertible finitary linear transformationsminimal subnormal irreducible subgroupsubdirect product of irreducible k- finitary linear groupstransitive group of finitary permutations

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) Local properties of groups (20E25) Subgroups of symmetric groups (20B35)

Related Items (23)

Linear groups with the minimal condition on subgroups of infinite central dimension. ⋮ Unnamed Item ⋮ Linear groups with rank restrictions on the subgroups of infinite central dimension. ⋮ Hypercentral unipotent finitary skew linear groups ⋮ The ideal lattices of the complex group rings of finitary special and general linear groups over finite fields ⋮ Groups of periodically defined linear transformations of an infinite-dimensional vector space ⋮ On modules over group rings of nilpotent groups. ⋮ Unnamed Item ⋮ Locally soluble AFA-groups. ⋮ Free products of finitary linear groups ⋮ On nonmodular periodic finitary linear groups ⋮ Finitary representations and images of transitive finitary permutation groups ⋮ Homomorphic images of finitary linear groups ⋮ On modules over integer-valued group rings of locally soluble groups with rank restrictions imposed on subgroups. ⋮ Infinite dimensional linear groups with many \(G\)-invariant subspaces. ⋮ Stabilizers of direct composition series. ⋮ Periodic Groups Covered by Transitive Subgroups of Finitary Permutations or by Irreducible Subgroups of Finitary Transformations ⋮ Inertial properties in groups ⋮ Locally nilpotent linear groups with restrictions on their subgroups of infinite central dimension. ⋮ On finitary series of groups represented as permutation or linear 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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• An identification theorem for the locally finite nontwisted Chevalley groups
• The classification of the simple periodic linear groups
• Finitary linear transformation groups and elements of finite local degree
• Infinite alternating groups as finitary linear transformation groups
• A note on finitary permutation groups
• Groups of finitary permutations
• The structure of finitary permutation groups
• The lawlessness of groups of finitary permutations
• Normal subgroups of finitary permutation groups
• On finite simple groups of characteristic 2 type
• Strong finiteness conditions in locally finite groups
• MONOMORPHISMS AND DIRECT LIMITS OF FINITE GROUPS OF LIE TYPE
• On the embedding of a group in a join of given groups

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