Question

Hello, could you please show all your steps without skipping any part. please show also all your defintion or anything that would enhancemy understanding of this question . Thanks in advance

we've covered in class in your explanation. 3) (4 marks) Find a group of permutations that is isomorphic to Z.. Explicitly define an isomorphism from Zs to this group of isomorphisms.

Answer 1

Consider, S5 : The group of permutations on 5 elements. Let G be the subgroup of Ss generated by the 5 - cycle a = (1 2 3 4 5); o(a) = 5. Define, :GZ5 by vla') := [i], where 0 <i< 4. This is the required isomorphism.