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Tridip Bhuyan posted an Question
August 12, 2021 • 07:27 am
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30 points
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)
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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).