Homomophim and cannoical map assignement due in 13 hours

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urgent homomophim and cannoical map assignement due in 13 hours

due now
 
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I believe you can use the first isomorphism theorem. What is the isomorphism it provides, and how can you connect it with subgroups of G that contain the kernel?
 


i think it is not the induced isomorphism between the factor group and the image.
i think its just the "image of a subgroup and the preimage of the image of a subgroup",right?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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