Hey I am having trouble with the following two questions:



For 4 it is easy enough to show S(i) is a subgroup however since these are sets of permutations, I am having trouble finding a function that shows isomorphism.
Then to argue that S(i,j) is not a subgroup is it correct that S(i,j) does not have an identity element? I'm unsure because I'm not too good with permutations

Then for 5, I'm unsure of how to use gcd(n,k) = 1 to proceed.

Can anyone help?