Understanding Centralizers and Centers in Groups for Algebra Students"

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elle
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Hi,
I'm currently self studying from an Algebra book but I'm having problems understanding the definition of the centralizer and center in a group :confused:

Like for example what is C(a) and Z(G) for the Quaternion group?

Can someone help? Many thanks!
 
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Do you mean to say you're having trouble computing them, or understanding them?
 
Both, would be very helpful if the definition was applied to the example excerise question I provided...
 

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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