Simple normal subgroup

This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property (itself viewed as a subgroup property): simple group
View a complete list of such conjunctions

Definition

Symbol-free definition

A subgroup of a group is termed a simple normal subgroup if it is simple as a group and normal as a subgroup.

Relation with other properties

Weaker properties

• Minimal normal subgroup
• Transitively normal subgroup
• Simple subnormal subgroup
• Component