Unformatted text preview: gx for '.g/.x/ . With this simpliﬁed notation, the homomorphism property reads like a mixed associative law: .g 2 g 1 /x D g 2 .g 1 x/ . Lemma 5.1.2. Given an action of G on X , deﬁne a relation on X by x ± y if there exists a g 2 G such that gx D y . This relation is an equivalence relation. Proof. Exercise 5.1.1 . n Deﬁnition 5.1.3. Given an action of G on X , the equivalence classes of the equivalence relation associated to the action are called the orbits of the action. The orbit of x will be denoted O .x/ . 237...
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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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