Free Group
The most general group generated by a set S is the group freely generated by S. Every group generated by S is isomorphic to a quotient of this group, a feature which is utilized in the expression of a group's presentation.
Read more about this topic: Generating Set Of A Group
Famous quotes containing the words free and/or group:
“I am truly free only when all human beings, men and women, are equally free. The freedom of other men, far from negating or limiting my freedom, is, on the contrary, its necessary premise and confirmation.”
—Mikhail Bakunin (1814–1876)
“We begin with friendships, and all our youth is a reconnoitering and recruiting of the holy fraternity they shall combine for the salvation of men. But so the remoter stars seem a nebula of united light, yet there is no group which a telescope will not resolve; and the dearest friends are separated by impassable gulfs.”
—Ralph Waldo Emerson (1803–1882)