Free basis of a group
= Free basis of a group
= Free bases of a group
{synonym}
A subset $X$ is a free basis of a <group> $G$ when the natural map from the <free group> on $X$ to $G$ is an <isomorphism>. Equivalently, $X$ generates $G$ and no nonempty freely reduced word in $X\cup X^{-1}$ equals the identity. A generating set is not automatically a free basis.