class equation
The conjugacy classes of a group form a partition
of its elements.
In a finite group
, this means that the order of the group is
the sum of the number of elements of the distinct conjugacy classes.
For an element of group ,
we denote the centralizer
in of by .
The number of elements in the conjugacy class of is ,
the index of in .
For an element of the center of ,
the conjugacy class of consists of the singleton .
Putting this together gives us the class equation
where the are elements of the distinct conjugacy classes contained in .
Title | class equation |
---|---|
Canonical name | ClassEquation |
Date of creation | 2013-03-22 13:10:41 |
Last modified on | 2013-03-22 13:10:41 |
Owner | yark (2760) |
Last modified by | yark (2760) |
Numerical id | 9 |
Author | yark (2760) |
Entry type | Theorem |
Classification | msc 20E45 |
Synonym | conjugacy class formula |
Related topic | ConjugacyClass |