In mathematics, the HNN extension is an important construction of combinatorial group theory.
Introduced in a 1949 paper Embedding Theorems for Groups[1] by Graham Higman, Bernhard Neumann, and Hanna Neumann, it embeds a given group G into another group G' , in such a way that two given isomorphic subgroups of G are conjugate (through a given isomorphism) in G' .