Unformatted text preview: x . Therefore  O ( x )  =  G/G x  = [ G : G x ]. ± Question : If y ∈ O ( x ) and g ∈ G x does that imply g ∈ G y ? Answer : No, not necessarily. y ∈ O ( x ) ⇒ α h ( x ) = y for some h ∈ G . g ∈ G x ⇒ α g ( x ) = x . What we know: α h α g α h1 ( y ) = α h α g ( x ) = α h ( x ) = y . So hgh1 ∈ G y . 1...
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This note was uploaded on 04/19/2011 for the course MATH 21373 taught by Professor Johnson during the Spring '11 term at Carnegie Mellon.
 Spring '11
 Johnson
 Algebra, Sets

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