Periodic 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): periodic group
View a complete list of such conjunctions

Statement

A subgroup of a group is termed a periodic normal subgroup if it satisfies the following two conditions:

• It is a normal subgroup of the whole group.
• It is a periodic group: every element has finite order.

Relation with other properties

Stronger properties

• Finite normal subgroup

Weaker properties

• Amalgam-characteristic subgroup: For proof of the implication, refer Periodic normal implies amalgam-characteristic and for proof of its strictness (i.e. the reverse implication being false) refer Amalgam-characteristic not implies periodic normal.
• Potentially characteristic subgroup
• Normal subgroup

Metaproperties

Quotient-transitivity

This subgroup property is quotient-transitive: the corresponding quotient property is transitive.
View a complete list of quotient-transitive subgroup properties