Free Product

The free product GH is the group whose elements are the reduced words in G and H, under the operation of concatenation followed by reduction.

For example, if G is the infinite cyclic group <x>, and H is the infinite cyclic group <y>, then every element of GH is an alternating product of powers of x with powers of y. In this case, GH is isomorphic to the free group generated by x and y.

Read more about Free Product:  Presentation, Generalization: Free Product With Amalgamation, In Other Branches

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