Conjugate (group theory)
Let be a group operating on a set
. An element
conjugate to an element
if there exists an element
such that
. The relation of conjugacy is an equivalence relation. The set of conjugates of an element
of
is called the orbit of
.
Note that this definition conforms to the notion of complex conjugate. Indeed, under the group of field automorphisms on the complexe numbers that do not change the reals, the orbit of a complex number is the set
.
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