Combinatorial Equivalence between Group Presentations
Sushil Jajodia · Proceedings of the American Mathematical Society · 1982
Let $\mathcal {P} = ({x_1}, \ldots ,{x_n}:{W_1}, \ldots ,{W_m})$ and $\mathcal {R} = ({x_1}, \ldots ,{x_n}:{R_1}, \ldots ,{R_m})$ be two presentations, with the same generators, for a group $\pi$. In this note, we give a necessary and sufficient criterion which insures the existence of a combinatorial equivalence between $\mathcal {P}$ and $\mathcal {R}$ requiring only replacement operations.