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:
“Each class of society has its own requirements; but it may be said that every class teaches the one immediately below it; and if the highest class be ignorant, uneducated, loving display, luxuriousness, and idle, the same spirit will prevail in humbler life.”
—First published in Girls’ Home Companion (1895)
“Jail sentences have many functions, but one is surely to send a message about what our society abhors and what it values. This week, the equation was twofold: female infidelity twice as bad as male abuse, the life of a woman half as valuable as that of a man. The killing of the woman taken in adultery has a long history and survives today in many cultures. One of those is our own.”
—Anna Quindlen (b. 1952)