Group presentation

Let \(S\) be a set, let \(F[S]\) be the free group on \(S\), and let \(R\subseteq F[S]\) be a set of words in \(S\). The group presented by generators \(S\) and relations \(R\) is \[ \gens{S \st R} \coloneqq F[S] / \cl_n(R), \] where \(\cl_n(R)\) is the normal closure of \(R\) in \(F[S]\), the smallest normal subgroup of \(F[S]\) containing \(R\). A presentation of a group \(G\) is an isomorphism \(G\cong\gens{S \st R}\).