Problem 4: Let G = Z° and let H be the subgroup of G generated by (2, 4, 4), (-6, 6, 12) and (10, 4, 16). • (a) Calculate the Smith normal form of the matrix 2 4 4 -6 6 12 10 4 16, • (b) Find the finitely generated abelian group in invariant factor form that G/H is isomorphic to.

Problem 4: Let G = Z° and let H be the subgroup of G generated by (2, 4, 4), (-6, 6, 12) and (10, 4, 16). • (a) Calculate the Smith normal form of the matrix 2 4 4 -6 6 12 10 4 16, • (b) Find the finitely generated abelian group in invariant factor form that G/H is isomorphic to.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Problem 4: Let G = Z° and let H be the subgroup of G generated by (2, 4, 4), (–6, 6, 12) and
(10, 4, 16).
• (a) Calculate the Smith normal form of the matrix
2 4
4
-6 6 12
10 4 16,
• (b) Find the finitely generated abelian group in invariant factor form that G/H is isomorphic to.

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