Existentially closed L\({\mathfrak X}\)-groups

zbMath0598.20036MaRDI QIDQ1079659

Felix Leinen

Publication date: 1986

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=RSMUP_1986__75__191_0

zbMATH Keywords

finitely generated subgroupsautomorphismslocally finite groupsisomorphism typescharacteristic subgroupssystem of equationsexistentially closed groupsverbally complete groupscharacteristically simplecountable e.c. L\({\mathfrak X}\)-groupslocally finite p-groupsnormal subgroup structurenormal subgroups totally ordered by inclusionunique chief series

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Periodic groups; locally finite groups (20F50) Chains and lattices of subgroups, subnormal subgroups (20E15) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Derived series, central series, and generalizations for groups (20F14) Local properties of groups (20E25)

Related Items (7)

Existentially closed locally finite p-groups ⋮ Die Automorphismengruppe der abzählbaren, existentiell abgeschlossenen \({\mathcal P}_ A\)-Gruppe \(E_ A\). (The automorphism group of the countable existentially closed \({\mathcal P}_ A\)-group \(E_ A)\) ⋮ Existentiell abgeschlossene Sylowturmgruppen. (Existentially closed Sylow tower groups) ⋮ Amalgamation of locally finite p-groups over a countable FC-group ⋮ Closure operators in topological groups related to von Neumann's kernel ⋮ Residually nilpotent groups whose closed subgroups are subnormal. ⋮ Countable existentially closed locally FC-groups

Cites Work

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• Radikale und koradikale Regeln
• Amalgams of \(p\)-groups.
• On the structure of standard wreath products of groups
• Residual Properties of Infinite Soluble Groups
• Some Constructions for Locally Finite Groups
• Embedding Theorems for Groups
• The Stability Group of a Series of Subgroups
• Endliche Gruppen I

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