Central subgroup of finite group

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

Relation with other properties

Weaker properties

• Finite-potentially verbal subgroup
  • Potentially verbal subgroup
  • Potentially fully characteristic subgroup
  • Finite-potentially characteristic subgroup
  • Potentially characteristic subgroup
• Finite central subgroup
• Finite normal subgroup
• Normal subgroup of finite group
• Central factor of finite group