Conjugacy Classes and Centralisers
By definition, the centre is the set of elements for which the conjugacy class of each element is the element itself, i.e. ccl(g) = {g}.
The centre is also the intersection of all the centralisers of each element of G. As centralisers are subgroups, this again shows that the centre is a subgroup.
Read more about this topic: Center (group Theory)
Famous quotes containing the word classes:
“Of all classes the rich are the most noticed and the least studied.”
—John Kenneth Galbraith (b. 1908)