Subgroup of finite abelian group

This article describes a property that arises as the conjunction of a subgroup property: subgroup with a group property imposed on the ambient group: finite abelian 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 finite abelian group is a subgroup of a finite abelian group.

Relation with other properties

Stronger properties

• Subgroup of finite cyclic group

Weaker properties

• Normal subgroup of finite group
• Subgroup of finite nilpotent group
• Subnormal subgroup of finite group
• Subgroup whose index of intersection with any subgroup divides the index of that subgroup
• Subgroup of finite solvable group
• Subgroup whose composition factors are a subset of the composition factors of the whole group