Lecture Notes on Bayesian Estimation and Classification
《Lecture Notes on Bayesian Estimation and Classification》 · 第 189 页 · Section 6.4「Generalized Free Products」，6.4.5 及其后定义
Let $H$ and $K$ be subgroups of a group $G$ and let $\theta:H\to K$ be an isomorphism. Then $G$ can be embedded in a group $G^*$ such that $\theta$ is induced by an inner automorphism of $G^*$. What is more, if $G$ is torsion-free, then so is $G^*$. […] The group $\langle t,G\rangle$ is called an HNN-extension of $G$ (after Higman, Neumann, and Neumann). It may be thought of as the group generated by $G$ and $t$ subject to the relations $x^t=x^\theta$, $(x\in H)$.