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Question

Consider the subgroup
S = {`0 , alpha , alpha^2 , alpha + alpha^2`} of `ZZ_2(alpha)`.
Which of the following statements is correct:
A) S is isomorphic to `ZZ_4` and has exactly one element of order 4.
B) S is isomorphic to `ZZ_2 times ZZ_2` and all non-zero elements have order 2. ?