Question:

For g ∈ Z\Z, let gˉ\bar{g} ∈ Z8\Z_8 denote the residue class of g modulo 8. Consider the group Z8×\Z^×_8 = {xˉ\bar{x} ∈ Z8\Z_8 : 1 ≤ x ≤ 7, gcd(x, 8) = 1} with respect to multiplication modulo 8. The number of group isomorphisms from Z8×\Z^×_8 onto itself is equal to ________

Updated On: Oct 1, 2024
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Correct Answer: 6

Solution and Explanation

The correct answer is 6.
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