Intermediately normality-large subgroup
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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
- It is normality-large in every intermediate subgroup
- It does not occur as a retract of any subgroup properly containing it.
Definition with symbols
- For any subgroup of containing , and any normal subgroup of such that is trivial, must be trivial
- If is a subgroup of containing , and is a retraction from to (i.e. a surjective homomorphism that restricts to the identity map on ), then .