Unformatted text preview: ∼ on the set of nonzero real numbers? (a) a ∼ b if and only if a / b ∈ Z . (b) a ∼ b if and only if a / b ∈ Q . (7 points) 7. Let G be the subset of Z 8 consisting of the elements [ 1 ] , [ 3 ] , [ 5 ] , [ 7 ] with the operation ± (modular multiplication). Compute the Cayley table of G . Which elements of G have an inverse? (8 points) 8. Determine the order of the element ± ( 1 2 3 4 5 6 )( 7 8 ) , ² [ 1 ] [ 1 ] [ ] [ 2 ] ³ ´ in S 8 × GL ( 2 , Z 3 ) . (8 points) Test on Tuesday, September 27. Material ﬁrst three chapters, that is up to section 14, approximately . Review session on Sunday September 25 at 4:50 p.m. in McBryde 126....
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 Fall '08
 PARRY
 Math, Algebra, Group Theory, Equivalence relation, Let, Cayley table

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