Finite group presentation
= Finite group presentation
{title2=$\langle X\mid R\rangle$}
A finite group presentation has finitely many generators and finitely many relators. It defines the quotient of the <free group> on $X$ by the <normal closure> of $R$. <Free products> of finitely presented groups and <HNN extensions> along explicitly finitely generated associated subgroups have finite presentations obtained by adjoining finitely many generators and relations.