Normal subgroup of periodic group

This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property imposed on the ambient group: periodic group
View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

Definition

A subgroup of a group is a normal subgroup of periodic group if the whole group is a periodic group (i.e., every element has finite order) and the subgroup is a normal subgroup.

Relation with other properties

Stronger properties

• Normal subgroup of finite group

Weaker properties

• Periodic-quotient normal subgroup
• Periodic normal subgroup
• Normal closure of periodic subset