Understanding Centralizers and Centers in Groups for Algebra Students"

[elle]

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

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

Can someone help? Many thanks!

 

[Hurkyl]

Do you mean to say you're having trouble computing them, or understanding them?

 

[elle]

Both, would be very helpful if the definition was applied to the example excerise question I provided...