Let
a be an element of a
group G. The
conjugacy class
of
a consists of all
conjugates of
a
Conj(a)={gag-1 such that
g in
G}
The conjugacy classes of the elements of G are equivalence classes
for the equivalence relation on G
given by aRb iff there exists x in G such that
b=xax-1. As such the conjugacy classes of G
partition G. See also centralizer.