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 \{(G_\alpha,\times)\}_{\alpha\in I} be an arbitrary family of subgroups of G that generate G. Suppose that:

  • \forall\alpha,\beta\in I[\alpha\ne\beta\implies G_\alpha\cap G_\beta=\{e\}] where e denotes the identity element of G

We say that G is the free product of \{G_\alpha\}_{\alpha\in I} if:

  • for all x\in G there exists only one reduced word that represents x