The growth series for Higman 3
Eric M. Freden, Jennifer L. Schofield · Journal of Group Theory · 2008
We generalize an example of Higman to a family of groups H m , m = 1, 2, 3, …, each of which is isomorphic to the amalgam of a solvable Baumslag–Solitar group with itself. We explicitly compute the growth function of H 3 . This function is algebraic but not rational. The construction uses the tree-like geometry of the Cayley graph and ideas from formal language theory. Modification of the proof allows the computation of the growth function of H m for odd m .