Unformatted text preview: factors for the abelian groups of order 44100. 44100 = 2 2 Â· 3 2 Â· 5 2 Â· 7 2 . Thus the number of abelian groups of order 44100 is 2 4 = 16. In the table below n will indicate Z / n Z ; thus using this notation there are two abelian groups of order p 2 , namely p 2 and p , p . Elementary Divisors Invariant Factors 2 2 , 3 2 , 5 2 , 7 2 44100 2 2 , 3 2 , 5 2 , 7 , 7 6300,7 2 2 , 3 2 , 5 , 5 , 7 2 8820,5 2 2 , 3 , 3 , 5 2 , 7 2 14700,3 2 , 2 , 3 2 , 5 2 , 7 2 22050,2 2 2 , 3 2 , 5 , 5 , 7 , 7 1260,35 2 2 , 3 , 3 , 5 , 5 , 7 2 2940,15 2 , 2 , 3 , 3 , 5 2 , 7 2 7350,6 2 2 , 3 , 3 , 5 2 , 7 , 7 2100,21 2 , 2 , 3 2 , 5 , 5 , 7 2 4410,10 2 , 2 , 3 2 , 5 2 , 7 , 7 3150,14 2 2 , 3 , 3 , 5 , 5 , 7 , 7 420,105 2 , 2 , 3 2 , 5 , 5 , 7 , 7 630,70 2 , 2 , 3 , 3 , 5 2 , 7 , 7 1050,42 2 , 2 , 3 , 3 , 5 , 5 , 7 2 1470,30 2 , 2 , 3 , 3 , 5 , 5 , 7 , 7 210,210...
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 Fall '07
 PALinnell
 Math, Algebra, Prime number, abelian groups, Sylow psubgroup

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