Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 104 / 1 / a

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- Solution a

Solution

Because the generating sets are disjoint, the free product has the presentation

G * H = ⟨ X ⊔ Y ∣ R ⊔ S ⟩ .

This is immediate from the universal property of a group presentation: a map out of this presented group is exactly a pair of homomorphisms from

G

and

H

to the target group.

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