Homocyclic normal subgroup

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.

Stronger properties

 * Weaker than::Cyclic normal subgroup
 * Weaker than::Cyclic normal subgroup of finite group
 * Weaker than::Homocyclic normal subgroup of finite group

Weaker properties

 * Stronger than::Abelian normal subgroup
 * Stronger than::Class two normal subgroup
 * Stronger than::Nilpotent normal subgroup