Unformatted text preview: x * x ′ = e . (Hint: calculate x ′ * ( x * x ′ )). 2. (a) Show that multiplication is a welldeFned binary operation on the set Z n of congruence classes of integers modulo n . (b) Given an integer n > 1, let Z ∗ n be the set of elements x ∈ Z n such that there exists y ∈ Z n with xy = 1. Show that Z ∗ n with the operation of multiplication is a group. (c) Write multiplication tables for Z ∗ 8 , Z ∗ 10 , and Z ∗ 12 . (d) Show that Z ∗ 8 and Z ∗ 12 are isomorphic, but that Z ∗ 10 is not isomorphic to Z ∗ 8 and Z ∗ 12 . 3. ±raleigh, section 4, exercises 9, 32, 41. 4. ±raleigh, section 5, exercises 13, 51, 54. 5. How challenging did you Fnd this assignment? How long did it take?...
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This note was uploaded on 03/14/2012 for the course MATH 113 taught by Professor Ogus during the Spring '08 term at Berkeley.
 Spring '08
 OGUS
 Math

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