profile-img
Tridip Bhuyan posted an Question
August 12, 2021 • 01:57 am 30 points
  • IIT JAM
  • Mathematics (MA)

Show that u(8) is isomorphic to u(12)

Please solve this show that U(8) is isomorphic to U(12)

1 Answer(s) Answer Now
  • 0 Likes
  • 1 Comments
  • 0 Shares
  • comment-profile-img>
    Irfan ansari 1 best-answer

    F:U(8)--->U(12) such that: F(1)=1´, F(3)=11´, F(5)=5´, F(7)=7´, Note that F is biyective. Now See that F is a isomorphism with the multiplication: F(1*n)=F(n) for all n in U(8), now, F(3*5)=F(15)=F(7)=7´=55´=11´*5´=F(3)*F(5). F(5*7)=F(35)=F(3)=11´=35´=5´*7´=F(5)*F(7). F(3*7)=F(21)=F(5)=5´=77´=11´*7´=F(3)*F(7). so F is a homomorphism and as F is biyective it implies than F is a isomorphism, then U(8) IS ISOMORPHIC TO U(12).

whatsapp-btn

Do You Want Better RANK in Your Exam?

Start Your Preparations with Eduncle’s FREE Study Material

  • Updated Syllabus, Paper Pattern & Full Exam Details
  • Sample Theory of Most Important Topic
  • Model Test Paper with Detailed Solutions
  • Last 5 Years Question Papers & Answers