4. Let p and q be distinct prime numbers and let n = p²q². Determineall the subgroups of Zn and draw the lattice diagram for subgroups.Justify your work.5. Let G be a cyclic group of order n, generated by a. Let m be an integersuch that ged(m, n) = 1. Prove that there exists a unique x E G suchthat r = a.6. Let n ≥ 2 be an integer.(a) If H≤ S, and H has an odd order, then H≤ An.(b) If a, 3 € Sn, prove that either both aßa-¹ and 3 are even or bothare odd.

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Answered: 4. Let p and q be distinct prime…

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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4. Let p and q be distinct prime numbers and let n = p²q². Determine all the subgroups of Zn and draw the lattice diagram for subgroups. Justify your work.