Question: Let G be a Z module generated by v 1 , v 2 ,v 3 subject to the relations 2v 1 - 4v 2 -

Let G be a Z module generated by v₁, v₂,v₃ subject to the relations

2v₁ - 4v₂ - 2v₃ = 0

10v₁ - 6v₂ + 4v₃ = 0

6v₁ - 12v₂ - 6v₃ = 0

Prove that there exists a set of generators w1,w2,w3 of G such that 2w1 = 0, 14w2 = 0 and w3 has infinite order, i.e. nw3 doesnot equal to 0 for every positive integer n.

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