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 !

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.

_________________Sometimes Truth is meanlingless;What means is how you believe in.

偶爾，真相並沒有意義；意義在於你怎樣相信。