# Amalgam-normal-subhomomorph-containing subgroup

From Groupprops

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

## Definition

A subgroup of a group is termed an **amalgam-normal-subhomomorph-containing subgroup** if the amalgamated subgroup is a normal-subhomomorph-containing subgroup in the amalgamated free product .

## Formalisms

### In terms of the in-amalgam operator

This property is obtained by applying the in-amalgam operator to the property: normal-subhomomorph-containing subgroup

View other properties obtained by applying the in-amalgam operator