Unformatted text preview: θ ([ 1 ]) = ( 1 2 3 )( 4 5 ) (don’t verify). Determine θ ([ 9 ]) . (6 points) 9. Let H = h ( 1 2 3 ) , ( 1 2 )( 3 4 ) i . (a) Prove that h ( 1 2 3 ) i is not a normal subgroup of H . (b) Prove that  H  6 = 6. (c) Prove that H ± S 4 . (6 points) 10. Let H ± G be groups and suppose every nonidentity element of G has order 5. Prove that every nonidentity element of G / H has order 5. (6 points) 11. Let G = Z 4 × Z 4 and let H = h [ 2 ] i×h [ 2 ] i . (a) Write down the right cosets of H in G . (b) Construct the Cayley table for G / H . (6 points) Test on Tuesday, November 1. Material sections 15–22 excluding 20 approximately . RSA encryption will not be examined. Review session on Sunday October 30 at 4:50 p.m. in McBryde 126....
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 Fall '08
 PARRY
 Math, Algebra, Group Theory, Normal subgroup, Subgroup, Cyclic group, Coset

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