(a) Define what it means for an abelian group to be finitely generated. Explain the terms...

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(a) Define what it means for an abelian group to be finitely generated. Explain the terms elementary divisors and rank of G and describe the structure theorem for finitely generated abelian groups. 2 46-8 1 32-1 (b) Consider the integral matrix R := 0-22 0 3 78-9 Determine the structure of the abelian group given by generators and relations AR(a1, a2, a3, a4 | Ro= 0) where a is the column vector (a1, a2, 03, 04). (c) Determine the number of elements of order 2 in AR in (b). [30 marks] (a) Define what it means for an abelian group to be finitely generated. Explain the terms elementary divisors and rank of G and describe the structure theorem for finitely generated abelian groups. 2 46-8 1 32-1 (b) Consider the integral matrix R := 0-22 0 3 78-9 Determine the structure of the abelian group given by generators and relations AR(a1, a2, a3, a4 | Ro= 0) where a is the column vector (a1, a2, 03, 04). (c) Determine the number of elements of order 2 in AR in (b). [30 marks]