Notes:Topology - Munkres/Section 68

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Section 68: Free Products of Groups

Content

Description: Words, reduction and reduced words

(page 412)

Definition: Free product

Let (G,×) be a group, let {(Gα,×)}αI be an arbitrary family of subgroups of G that generate G. Suppose that:

  • α,βI[αβGαGβ={e}] where e denotes the identity element of G

We say that G is the free product of {Gα}αI if:

  • for all xG there exists only one reduced word that represents x