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RESEARCH PRODUCT
Existentially closed locally cofinite groups
Felix Leinensubject
Normal subgroupIdentity (mathematics)Class (set theory)Transfer (group theory)Pure mathematicsIntersectionClosure (mathematics)General MathematicsComputingMethodologies_DOCUMENTANDTEXTPROCESSINGCountable setTopological groupGeneralLiterature_REFERENCE(e.g.dictionariesencyclopediasglossaries)Mathematicsdescription
Let be a class of finite groups. Then a c-group shall be a topological group which has a fundamental system of open neighbourhoods of the identity consisting of normal subgroups with -factor groups and trivial intersection. In this note we study groups which are existentially closed (e.c.) with respect to the class Lc of all direct limits of c-groups (where satisfies certain closure properties). We show that the so-called locally closed normal subgroups of an e.c. Lc-group are totally ordered via inclusion. Moreover it turns out that every ∀2-sentence, which is true for countable e.c. L-groups, also holds for e.c. Lc-groups. This allows it to transfer many known properties from e.c. L-groups to e.c. Lc-groups.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1992-06-01 | Proceedings of the Edinburgh Mathematical Society |