# Amalgam-strictly characteristic subgroup

From Groupprops

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

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 **amalgam-strictly characteristic** if the amalgamated subgroup is a strictly characteristic 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: strictly characteristic subgroup

View other properties obtained by applying the in-amalgam operator

## Relation with other properties

### Stronger properties

- Amalgam-normal-subhomomorph-containing subgroup
- Central subgroup:
`For full proof, refer: Central implies amalgam-strictly characteristic` - Normal subgroup contained in the hypercenter:
`For full proof, refer: Normal subgroup contained in the hypercenter is amalgam-strictly characteristic`