Amalgamated free factor

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]

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VIEW FACTS THAT:use, or start with, a subgroup satisfying the property|prove, or show that, a subgroup satisfies the property

Definition

A subgroup $H$ of a group $G$ is termed an amalgamated free factor if either $H$ is trivial or it is a factor in an internal amalgamated free product that is not of the form $H*_{G}G$ -- in other words, there exists a proper subgroup $K$ of $G$ such that $G$ is the internal amalgamated free product of $H$ and $K$ over $H\cap K$.

Relation with other properties

Stronger properties

• Free factor