Abelian Sylow subgroup

From Groupprops
Jump to: navigation, search
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 Abelian pronormal subgroup|FULL LIST, MORE INFO