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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]
A subgroup of a group is termed intermediately conjugacy-closed-to-retract if, whenever it is a conjugacy-closed subgroup in any intermediate subgroup, it is also a retract of that intermediate subgroup, i.e., it has a normal complement in the intermediate subgroup.
Relation with other properties
- Sylow subgroup: For full proof, refer: Sylow implies intermediately conjugacy-closed-to-retract