Finite-intersection-closedness is left residual-preserved
This article gives the statement, and possibly proof, of a subgroup metaproperty (i.e., Intersection-closed subgroup property (?)) satisfying a subgroup metametaproperty (i.e., Left residual-preserved subgroup metaproperty (?))
View all subgroup metametaproperty satisfactions View all subgroup metametaproperty dissatisfactions
Statement
Property-theoretic statement
The Left residual operator for composition (?) of a finite-intersection-closed subgroup property by any subgroup property is again finite-intersection-closed.
Related facts
Similar facts about being left residual-preserved
Some similar results about being left residual-preserved:
- Finite-join-closedness is left residual-preserved
- Join-closedness is left residual-preserved
- Intersection-closedness is left residual-preserved
- Normalizing join-closedness is left residual-preserved
- Conjugate-join-closedness is left residual-preserved
- Finite-conjugate-join-closedness is left residual-preserved
Similar facts about being right residual-preserved
Some related examples of right residual-preserved subgroup metaproperties: