Normal Sylow subgroup
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: normal subgroup and Sylow subgroup
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- It is a Sylow subgroup, and is normal in the whole group.
- It is a Sylow subgroup, and is subnormal in the whole group.
- It is a Sylow subgroup, and is characteristic in the whole group.
- It is a Sylow subgroup, and is fully characteristic in the whole group.
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Relation with other properties
- Nilpotent normal subgroup
- Nilpotent characteristic subgroup
- Normal Hall subgroup
- Complemented normal subgroup
- Fully characteristic subgroup
- Characteristic subgroup
- Intermediately characteristic subgroup
- Isomorph-free subgroup
- Intermediately fully characteristic subgroup
- Image-closed characteristic subgroup
- Image-closed fully characteristic subgroup
- Normal subgroup
YES: This subgroup property satisfies the transfer condition: if a subgroup has the property in the whole group, its intersection with any subgroup has the property in that subgroup.
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Intermediate subgroup condition
YES: This subgroup property satisfies the intermediate subgroup condition: if a subgroup has the property in the whole group, it has the property in every intermediate subgroup.
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YES: This subgroup property satisfies the image condition, i.e., under any surjective homomorphism, the image of a subgroup satisfying the property also satisfies the property
View other subgroup properties satisfying image condition