Homocyclic 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): homocyclic group
View a complete list of such conjunctions

Definition

A subgroup of a group is termed a homocyclic normal subgroup if it is a normal subgroup of the whole group and is also a homocyclic group as an abstract group. In other words, it is a direct product of pairwise isomorphic cyclic groups.

Relation with other properties

Stronger properties

• Cyclic normal subgroup
• Cyclic normal subgroup of finite group
• Homocyclic normal subgroup of finite group

Weaker properties

• Abelian normal subgroup
• Class two normal subgroup
• Nilpotent normal subgroup