Can someone help me with the following problem?

Let G be the cyclic group <a> of order 5.

1. Write out the elements of a group of permutations that is isomorphic to G.

2. Exhibit an isomorphism from G to this group.

Thanks.

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- Jun 1st 2009, 09:01 PMyvonnehr[SOLVED] Using Cayley's Theorem
Can someone help me with the following problem?

Let G be the cyclic group <a> of order 5.

1. Write out the elements of a group of permutations that is isomorphic to G.

2. Exhibit an isomorphism from G to this group.

Thanks. - Jun 1st 2009, 10:58 PMGamma
Well you know it should be isomorphic to a subgroup of and it needs to be cyclic, so you need only find an element of which has order 5. (1 2 3 4 5) is a good choice, the isomorphism is as follows: