Prehomomorph-contained subgroup of finite group

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This article describes a property that arises as the conjunction of a subgroup property: prehomomorph-contained 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 prehomomorph-contained subgroup of finite group if the whole group is a finite group and the subgroup is a prehomomorph-contained subgroup of it -- for any surjective homomorphism from another subgroup to it, it is contained in the other subgroup.

Relation with other properties

Weaker properties

• Isomorph-free subgroup of finite group
• Characteristic subgroup of finite group
• Normal subgroup of finite group