Question #203253

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

order 12 is isomorphic


1
Expert's answer
2021-06-07T15:04:52-0400

Answer:-


We have given cyclic group G=<a>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 S12S_{12} generated by the cycle , that is (1,2,3,4,5,6,7,8,9,10,11,12)(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.


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