= Independence of finite presentation from finite generators
Suppose $G=\langle Y\mid R(Y)\rangle$ is a finite <group presentation>, and $X$ is any finite generating set. Write $y_j=u_j(X)$ and $x_i=v_i(Y)$. A finite presentation on $X$ is obtained using the relators $R(u(X))$ and $x_i=v_i(u(X))$. The substitutions in both directions give inverse homomorphisms, proving that finite presentability does not depend on the finite generators chosen.
// Target: geometry-and-topology.bigb
Back to article page
