Class Equation
An important result about orders is the class equation; it relates the order of a finite group G to the order of its center Z(G) and the sizes of its non-trivial conjugacy classes:
where the di are the sizes of the non-trivial conjugacy classes; these are proper divisors of |G| bigger than one, and they are also equal to the indices of the centralizers in G of the representatives of the non-trivial conjugacy classes. For example, the center of S3 is just the trivial group with the single element e, and the equation reads |S3| = 1+2+3.
Read more about this topic: Order (group Theory)
Famous quotes containing the words class and/or equation:
“Thats how the Germans are.... The aristocrats at the top hard as glass, cold as ice, servants of the King, the working masses willing, pliable, sentimental, susceptible to brutality, the middle class educated and cowardly to the point of servility.”
—Alfred Döblin (18781957)
“A nation fights well in proportion to the amount of men and materials it has. And the other equation is that the individual soldier in that army is a more effective soldier the poorer his standard of living has been in the past.”
—Norman Mailer (b. 1923)