LERF group

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

Definition

A group is termed a LERF group or locally extended residually finite group or subgroup-separable group if every finitely generated subgroup is a closed subset in the profinite topology.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Finite group |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Residually finite group The trivial subgroup is closed |FULL LIST, MORE INFO
Locally residually finite group Residually finite group|FULL LIST, MORE INFO