# Prehomomorph-contained subgroup of finite group

From Groupprops

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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 theambient 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.