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sheep

Joined: 14 Oct 2004Posts: 1

Posted: Thu Oct 14, 2004 12:49 pm    Post subject: algebra problem

Can somebody help me ? ^.^ 1. Suppose G is a cyclic group with order n,

a. Prove that if r,s are relatively prime, then Crxs is isomorpsic to CrXCs.

b. Prove that if r is prime, then Crxr is not isomorphic to CrXCr.

Thanks a lot !

Milton

Frequent VisitorJoined: 27 Oct 2003Posts: 176

Location: HKUST Math

Posted: Thu Oct 14, 2004 11:53 pm    Post subject:

Let and be the generator of and . (a) follows from noting that is the generator of , which is of order .

To prove (b), note that is not cyclic as its elements have order not greater than . It seems we do not need to be prime here.

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