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:
“I struck the board, and cried, “No more.
I will abroad.”
What? Shall I ever sigh and pine?
My lines and life are free; free as the road,
Loose as the wind, as large as store.
Shall I be still in suit?”
—George Herbert (1593–1633)
“Perhaps I am still very much of an American. That is to say, naïve, optimistic, gullible.... In the eyes of a European, what am I but an American to the core, an American who exposes his Americanism like a sore. Like it or not, I am a product of this land of plenty, a believer in superabundance, a believer in miracles.”
—Henry Miller (1891–1980)