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Question

Linear Algebra Question on Groups

For a positive integer n, let U(n) = {rˉ\bar{r} ∈ ℤn ∶ gcd(r, n) = 1} be the group under multiplication modulo n. Then, which one of the following statements is TRUE ?

A

U(5) is isomorphic to U(8)

B

U(10) is isomorphic to U(12)

C

U(8) is isomorphic to U(10)

D

U(8) is isomorphic to U(12)

Answer

U(8) is isomorphic to U(12)

Explanation

Solution

The correct option is (D) : U(8) is isomorphic to U(12).