Answer to Question #203253 in Abstract Algebra for Anand

Question

Using Cayley’s theorem, find the permutation group to which a cyclic group of 

order 12 is isomorphic

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.