#8 4:35AAA s3.amazonaws.comChapter 5 Homework1. What is the order of a - (4,a.4)? What is the order of "- (4,a,..a.)?2. What is the order of the following permutations?2 3 4 56 1 2 42 3 4 56Y2 15 4 6 3)3. Decompose the following into a product of disjoint cycles:(1 2 3 4 5 6"2 15 4 6 3)"(1 2 3 4 5B."3 6 1 2 4 s4. Decompose the following into a product of transpositions:(1 22 15 462 3 4 55. If a is an even permutation, then a" is even. If « is an oddpermutation, then a" is also odd.6. Prove that the product of an even permutation and an oddpermutation is odd.7. Show that 4 is a subgroup of $.8. Show that " "B "uß is an even permutation for any permutations ".9. In the group $, find elements a and b such that |a| = 2 = |b| and |ab| =3.10. In S., find a cyclic subgroup of order 4 and a non-cyclic subgroupof order 4. Hint: use Table 5.1.

Name: #8 4:35AAA s3.amazonaws.comChapter 5 Homework1. What is the order of a
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Description: #8 4:35AAA s3.amazonaws.comChapter 5 Homework1. What is the order of a - (4,a.4)? What is the order of "- (4,a,..a.)?2. What is the order of the following permutations?2 3 4 56 1 2 42 3 4 56Y2 15 4 6 3)3. Decompose the following into a product of dis