Which of the following is not correct? a) U(14) is isomorphic to S3 b) U(14) is isomorphic to U(7) c) U(8) is isomorphic to U(12) d) none of these

Question

Which of the following is not correct? a) U(14) is isomorphic to S3 b) U(14) is isomorphic to U(7) c) U(8) is isomorphic to U(12) d) none of these

Stella Calderon · Accepted Answer

Step 1  U(14)={1,3,5,9,11,13}  (S3)=3≠6  1) So, the group have the same order  2) U(14) is abelian, and S3 is non abelian. But if two group are isomorphie, they are either both abelian or both non abelian  So, option A is incorrect.

nghodlokl · Accepted Answer

Step 1  U(8)={1,3,5,7}  U(12)={1,5,7,11}  U(14)={1,3,5,9,11,13}  U(7)={1,2,3,4,5,6}  (3)={1, (1,2),(1,3),(2,3),(1,2,3),(1,3,2)}  Hence U(8)=∼U(12), U(14)=∼U(7)  Also U(14)=∼S3 because have are non abelidn of equal  ⇒ Thus  None of there  U(n)={x×x&amp;lt;n and gcd(n,x)=1}

Which of the following is not correct?a) U(14) is isomorphic

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