Key Properties
Since the presentation for contains all the generators and relations from the presentation for, there is a natural homomorphism, induced by the identification of generators, which takes to . Higman, Neumann and Neumann proved that this morphism is injective, that is, an embedding of into . A consequence is that two isomorphic subgroups of a given group are always conjugate in some overgroup; the desire to show this was the original motivation for the construction.
Read more about this topic: HNN Extension
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