Presentation of A Group - Constructions

Constructions

Suppose G has presentation <S|R> and H has presentation <T|Q> with S and T being disjoint. Then

• the free product G ∗ H has presentation <S,T|R,Q> and
• the direct product G × H has presentation <S,T|R,Q, >, where means that every element from S commutes with every element from T (cf. commutator).