Group in which every weakly pronormal subgroup is pronormal
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 in which every weakly pronormal subgroup is pronormal is a group satisfying the condition that every weakly pronormal subgroup of it is a pronormal subgroup.
Relation with other properties
Stronger properties
- Solvable group: For proof of the implication, refer Solvable implies every weakly pronormal subgroup is pronormal and for proof of its strictness (i.e. the reverse implication being false) refer Every weakly pronormal subgroup is pronormal not implies solvable.
- Nilpotent group
- Group satisfying normalizer condition
- Hyper-N-group
- Group in which every subgroup is pronormal