Re: Centralizers, Normalizers and the Center

Write out the definition of each one above the other then start with a
few groups of small order and explicitly calculate each of them for
each group and all their subgroups. I think you'll see very clearly
what the relationship is. I recently had to convince myself of the
same thing and used the Quarternion group of order 8, the symetric
group of order 6, the Dihedral groups of order 8 and 16, they Klein 4
group, and they cyclic group of order 8 calculating each of these in
order to get a better understanding of what they were. I recommend the
same for you as well.

.

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