Unformatted text preview: Deﬁnition 2.6.16. Let a and b be elements of a group G . We say that b is conjugate to a if there is a g 2 G such that b D gag ± 1 . You are asked to show in the Exercises that conjugacy is an equivalence relation and to ﬁnd all the conjugacy equivalence classes in several groups of small order. Deﬁnition 2.6.17. The equivalence classes for conjugacy are called conjugacy classes. Note that the center of a group is related to the notion of conjugacy in the following way: The center consists of all elements whose conjugacy class is a singleton. That is, g 2 Z.G/ , the conjugacy class of g is f g g ....
View
Full Document
 Fall '08
 EVERAGE
 Algebra, Sets, Equivalence relation, equivalence class, Coset

Click to edit the document details