In
mathematics, specifically
group theory, the
free product is an operation that takes two
groups G and
H and constructs a new group
G *
H. The result contains both
G and
H as
subgroups, is
generated by the elements of these subgroups, and is the “most general” group having these properties. Unless one of the groups
G and
H is trivial, the free product is always infinite. The construction of a free product is similar in spirit to the construction of a
free group (the most general group that can be made from a given set of generators).