HNN Extension - Construction

Construction

Let be a group with presentation, and let be an isomorphism between two subgroups and of . Let be a new symbol not in, and define

G*_{\alpha} = \langle S,t \mid R, tht^{-1}=\alpha(h), \forall h\in H\rangle.

The group is called the HNN extension of relative to . The original group G is called the base group for the construction, while the subgroups and are the associated subgroups. The new generator is called the stable letter.

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