Definition:Free Group on Set

Definition
Let $X$ be a set.

A free group on $X$ is a certain $X$-pointed group, that is, a pair $\struct {F, \iota}$ where:
 * $F$ is a group
 * $\iota : X \to F$ is a mapping

that can be defined as follows:

Also see

 * Equivalence of Definitions of Free Group on Set


 * Definition:Free Abelian Group on Set
 * Definition:Free Monoid