 Solution

A group presentation $⟨X\mid R⟩$ denotes the quotient $F(X)/⟨⟨R⟩⟩$ of the free group on the generator symbols by the normal closure of the relator words. The symbols generate the quotient, and each relator becomes the identity. The phrase also asserts that no additional relations are imposed except consequences of these relators and the group axioms. Equivalently, an assignment of the generators to a group extends to a group homomorphism from the presented group exactly when all relators evaluate to the identity; this is the universal property of a group presentation.