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Unformatted text preview: . This shows that [ 14 ] ∈ ker θ . 3. Since [ 14 ] 6 = [ 1 ] , the proof of previous result also shows that o ([ 14 ]) = 3. Therefore 3 ± ±  ker θ  by Lagrange’s theorem, say  ker θ  = 3 n where n is a positive integer. By the Fundamental Homomorphism Theorem,  C  =  Z # 211 / ker θ  = 210 /  ker θ  = 70 / n . Therefore  C  n = 70 and we conclude that  C  ± ± 70....
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This note was uploaded on 01/02/2012 for the course MATH 3124 taught by Professor Parry during the Fall '08 term at Virginia Tech.
 Fall '08
 PARRY
 Math, Algebra

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