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Unformatted text preview: (b) Compute 5 99 mod 21. 5. [14 Points] Let G = Z / 16 = f 1 ; 3 ; 5 ; 7 ; 9 ; 11 ; 13 ; 15 g , where, as usual the group operation is multiplication modulo 16. Determine (with justication) if the following subsets of G are subgroups. (a) H = f 1 ; 3 ; 9 ; 11 g . (b) K = f 1 ; 5 ; 9 ; 11 g . 6. [14 Points] Answer the following questions concerning a cyclic group G = [ a ] with o ( a ) = 24. (a) What is the order j G j of G . (b) What is the order of the element a 20 . (c) How many subgroups of G are there? Be sure to include f e g and G in your count. (d) Is the group G Z 7 cyclic? Explain. 7. [16 Points] Find the smallest positive solution to the system of simultaneous linear congruences: x 9 mod 11 x 3 mod 9 : Math 4023 September 23, 2011 1...
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This document was uploaded on 12/28/2011.
 Fall '09

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