The free product G ∗ H 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 G ∗ H is an alternating product of powers of x with powers of y. In this case, G ∗ H 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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