Interesting group theory problem

betty2301
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Homework Statement


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Homework Equations


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The Attempt at a Solution


i can do part a.
can you give me hints on part b and c?
 

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For (b), you are asked to show that the sizes of these two sets are the same: \{gag^{-1} | g \in G\} and G / C(a). The natural thing to do is to try to find a bijection between the two. There's only one obvious candidate that I can see.
 

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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