Consider the Group (21,⊗21). a) Determine the order of this Group. b) List the complete set of elements of this Group. c) Construct the Cayley table of the Group. d) Determine if two distinct subgroups have the same order. The Group (Un,⊗n): For a positive integer n and a and b elements of Un, define
a ⊗n b := (a * b) mod n.
my answer is: List of element of G = [1, 11, 16, 17, 8, 19, 2, 13, 4, 5, 10, 20] Order of the Group = 12 I wrote down the Cayley table too.
I need help with item d) about the subgroups.
Any help would be great. Please let me know if the elements of the Group are correct?