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
Famous quotes containing the words free and/or product:
“... the most important effect of the suffrage is psychological. The permanent consciousness of power for effective action, the knowledge that their own thoughts have an equal chance with those of any other person ... this is what has always rendered the men of a free state so energetic, so acutely intelligent, so powerful.”
—Mary Putnam Jacobi (1842–1906)
“Poetry, whose material is language, is perhaps the most human and least worldly of the arts, the one in which the end product remains closest to the thought that inspired it.... Of all things of thought, poetry is the closest to thought, and a poem is less a thing than any other work of art ...”
—Hannah Arendt (1906–1975)