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Unformatted text preview: Denition 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 nd all the conjugacy equivalence classes in several groups of small order. Denition 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 ....
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra, Sets

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