|
|
|
The generators of a group 
are defined to be the smallest subset of group elements such that all other elements of
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