Normal Sylow subgroup

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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: normal subgroup and Sylow subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

A subgroup of a finite group is termed a normal Sylow subgroup if it satisfies the following equivalent conditions:

Examples

VIEW: subgroups satisfying this property | subgroups dissatisfying property normal subgroup | subgroups dissatisfying property Sylow subgroup
VIEW: Related subgroup property satisfactions | Related subgroup property dissatisfactions

Relation with other properties

Stronger properties

Weaker properties

Metaproperties

Transfer condition

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.
View other subgroup properties satisfying the transfer condition

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.
ABOUT THIS PROPERTY: View variations of this property satisfying intermediate subgroup condition | View variations of this property not satisfying intermediate subgroup condition
ABOUT INTERMEDIATE SUBROUP CONDITION:View all properties satisfying intermediate subgroup condition | View facts about intermediate subgroup condition

Image condition

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