Complete existentially closed locally finite groups

DOI10.1007/BF01194072zbMath0563.20037MaRDI QIDQ1057365

Simon Thomas

Publication date: 1985

Published in: Archiv der Mathematik (Search for Journal in Brave)

zbMATH Keywords

normal subgroupslocally finite groupsuniversal locally finite groupsexistentially closed groupscharacteristically simplecomplete locally finite p-groupsJensen's principlelocally finite \(\pi \) -groupslocally finite-soluble \(\pi \) -groupsuncountable subgroups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Periodic groups; locally finite groups (20F50) Model-theoretic algebra (03C60) Chains and lattices of subgroups, subnormal subgroups (20E15) Automorphism groups of groups (20F28) Local properties of groups (20E25)

Related Items (10)

Existentially closed L\({\mathfrak X}\)-groups ⋮ Existentially closed locally finite p-groups ⋮ Existentially closed locally FC-groups ⋮ Ideals in the multiplication algebra of a non-associative K-algebra ⋮ On torsion groups with nilpotent automorphism groups ⋮ McLain groups over arbitrary rings and orderings ⋮ Outer automorphisms of hypercentral p-groups ⋮ Unbounded actions of metric groups and continuous logic ⋮ Torsion-free nilpotent groups and E-modules ⋮ Countable existentially closed locally FC-groups

Cites Work

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• Existenziell abgeschlossene lokal endliche p-Gruppen
• Uncountable universal locally finite groups
• Existentially closed structures and Jensen's principle \(\diamond\)
• Model theory for infinitary logic. Logic with countable conjunctions and finite quantifiers
• Some Constructions for Locally Finite Groups
• Embedding Theorems for Groups
• Complete Universal Locally Finite Groups

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