Amalgamated free factor

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 $$H \cap K$$.

Stronger properties

 * Weaker than::Free factor