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sheep
Joined: 14 Oct 2004Posts: 1
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Posted: Thu Oct 14, 2004 12:49 pm Post subject: algebra problem
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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 !
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Milton
Frequent VisitorJoined: 27 Oct 2003Posts: 176
Location: HKUST Math
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Posted: Thu Oct 14, 2004 11:53 pm Post subject:
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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。
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