Subgroup of finite cyclic 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 cyclic 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 termed a subgroup of finite cyclic group if the whole group is a finite cyclic group.

Relation with other properties

Weaker properties

• Variety-containing subgroup of finite group
  • Homomorph-containing subgroup of finite group
• Quotient-variety-containing subgroup of finite group
  • Quotient-homomorph-containing subgroup of finite group
• Prehomomorph-contained subgroup of finite group
• Isomorph-free subgroup of finite group
• Fully invariant subgroup of finite group
• Characteristic subgroup of finite group
• Normal subgroup of finite group
• Subgroup of finite abelian group
  • Subgroup of abelian group
  • Subgroup of finite nilpotent group
  • Subgroup of nilpotent group