LERF group
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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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 | |FULL LIST, MORE INFO |