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Conjugacy class
In group theory, equivalence class under the relation of conjugation / From Wikipedia, the free encyclopedia
In mathematics, especially group theory, two elements and
of a group are conjugate if there is an element
in the group such that
This is an equivalence relation whose equivalence classes are called conjugacy classes. In other words, each conjugacy class is closed under
for all elements
in the group.
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Members of the same conjugacy class cannot be distinguished by using only the group structure, and therefore share many properties. The study of conjugacy classes of non-abelian groups is fundamental for the study of their structure.[1][2] For an abelian group, each conjugacy class is a set containing one element (singleton set).
Functions that are constant for members of the same conjugacy class are called class functions.