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Free Group

The generators of a group $G$ are defined to be the smallest subset of group elements such that all other elements of $G$ can be obtained from them and their inverses. A Group is a free group if no relation exists between its generators (other than the relationship between an element and its inverse required as one of the defining properties of a group). For example, the additive group of whole numbers is free with a single generator, 1.

See also Free Semigroup

© 1996-9 Eric W. Weisstein