An amalgamated free product of groups 
and 
over a group 
, with specified injective homomorphisms 
and 
, is the quotient
 |
The denominator is the normal closure, so the two copies of each element of 
are identified. The canonical maps from 
and 
into this quotient are injective
(Brown 1982). For trivial 
it reduces to the free product.
The construction supplies the ambient group in the fixed
price problem.
