Answer to Question #196088 in Abstract Algebra for giughu

Question

Using Cayley’s theorem, what is the permutation group to which a cyclic group of order 12 is isomorphic to?

Answer 1

Answer:-

We have given cyclic group G = <a> of the order 12 generated by the element 'a’ of G,

we will take the' permutation group as we we have the cyclic subgroup H of S_12 generated by the cycle , that is (1,2,3,4,5,6,7,8,9,10,11,12) of the length 12 and

This (or a conjugate of it) is what we obtain as by the proof of the Cayley's Theorem.