[數學] 有關Groups的問題

[數學] 有關Groups的問題

jocelyn 於 星期五 十月 06, 2006 2:43 am


1.Explain why R^3 is not a group with respect to the cross-product X?
2.Let G be a group and X on the set G an element of finite order n=ord(x). Prove that for any greater and equal to 1 we have : ord(x^k) = n / (k,n)
[Hint: To show that n/(k,n)|ord(x^k) , use Euclid's Lemma]
3. Let T be the equilateral triangle with vertice v1=(0,0) , v2=(1,0) and v3=(1/2,root(3)/2)
for each element isom on the set SUM of T, determine the associated permutation of the vertices.
4.Find the orders of the following permutations:
a=(1234)(234)(456)     b=(12478)(178)(245)(23)      c=(12)(23)(34)(25)(45)

jocelyn
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