display | more...
The centralizer of an element a in a group G consists of all those elements of the group that commute with a
C(a)={x in G such that xa=ax}.

If the group is finite then we have the formula |C(a)|.|Conj(a)|=|G|, where Conj(a) is the conjugacy class of a.

There is a similar notion for rings.

Log in or register to write something here or to contact authors.