Definition:Free Group on Set/Definition 2

Definition

Let $X$ be a set.

The free group on $X$ is the pair $\struct {F, \iota}$ such that:

$F$ is the group of reduced group words on $X$

$\iota : X \to F$ is the canonical injection.

Also see

• Equivalence of Definitions of Free Group on Set

• Results about free groups can be found here.

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