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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.

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.

Advanced Engineering Mathematics
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. 5. Let G be a cyclic group of order n, generated by a. Let m be an integer such that ged(m, n) = 1. Prove that there exists a unique x E G such that 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 both are odd.
Transcribed Image Text: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. 5. Let G be a cyclic group of order n, generated by a. Let m be an integer such that ged(m, n) = 1. Prove that there exists a unique x E G such that 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 both are odd.
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