hw28 - j,n Exercise 83 In the last homework we saw that...

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Intro to Abstract Math Homework 28 Fall 2009 Due November 30 Exercise 81. Let G be a group and a G . Suppose | a | = n . Prove that if k N and k | n then | a k | = n/k . Exercise 82. Let G be a group, a G and | a | = n . Recall that for any k Z , h a k i = h a gcd( k,n ) i . Use this to prove that h a i i = h a j i if and only if gcd( i,n ) = gcd(
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Unformatted text preview: j,n ). Exercise 83. In the last homework we saw that U (25) is a group under multiplication modulo 25. a. List the elements of U (25). b. Given that U (25) = h 2 i , find all the generators of U (25)....
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This note was uploaded on 02/29/2012 for the course MATH 3326 taught by Professor Ryandaileda during the Fall '09 term at Trinity University.

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