Abelian Sylow subgroup
This article describes a property that arises as the conjunction of a subgroup property: Sylow subgroup with a group property (itself viewed as a subgroup property): abelian group
View a complete list of such conjunctions
Definition
A subgroup of a group is termed an abelian Sylow subgroup if it is abelian as a group and is also a Sylow subgroup of the whole group.
Relation with other properties
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Sylow subgroup | |FULL LIST, MORE INFO | |||
| abelian pronormal subgroup | abelian and a pronormal subgroup | |FULL LIST, MORE INFO | ||
| SCDIN-subgroup (not standard terminology) | any conjugation between two subsets in the subgroup via an element of the whole group can also be realized via an element in the normalizer of the subgroup | abelian and Sylow implies SCDIN | |FULL LIST, MORE INFO |