Must the center of a group be made up of congugacy classes?

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- May 13th 2011, 12:51 PMalexandrabel90Centers
Must the center of a group be made up of congugacy classes?

- May 13th 2011, 06:56 PMDrexel28
What does this mean? Is it true that the center of a group is a union of conjugacy classes? The answer is yes for two reasons. The first reason is the fact that for any group (since where where is the inner automorphism) and normal subgroups are subgroups which are unions of conjugacy classes. Perhaps simpler is the fact that, by definition, where is the conjugacy class of and the square union is just a fancy way of saying that the sets in the union are pairwise disjoint.