YLL討論網

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.