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Isomorphism types of abelian groups

  1. Nov 25, 2012 #1
    wrtie down the possible isomorphism types of abelian groups of orders 74 and 800

    then for 74=2*37 then Z(74) is isomorphism to Z2 * Z37 (by chinese remainder theorem) then for 74 , 2 we have Z74 and Z2*Z37 (i am not sure it is right or wrong
    then for 800 i know i should apply the fundamental theorem of fintely generated abelian groups, but i am not quite understand the methods of it , can someone help me the 800 case??????
     
  2. jcsd
  3. Nov 25, 2012 #2
    What does the fundamental theorem say? What have you tried so far?
     
  4. Nov 25, 2012 #3
    for 800=2^5*5^2 then there are two abelian groups of order 25:Z25,Z5xZ5, for2^5 ,we have 6 abelian groups : Z32,Z16xZ2,Z8xZ4,Z4xZ4xZ2,Z4xZ2xZ2xZ2,Z2xZ2xZ2xZ2xZ2

    so we get 12 different groups:
    Z25xZ32
    Z25xZ16xZ2
    Z25xZ8xZ4
    Z25xZ4xZ4xZ2
    Z25xZ4xZ2xZ2xZ2
    Z25xZ2xZ2xZ2xZ2xZ2
    Z5xZ5xZ32
    Z5xZ5xZ16xZ2
    Z5xZ5xZ8xZ4
    Z5xZ5xZ4xZ4xZ2
    Z5xZ5xZ4xZ2xZ2xZ2
    Z5xZ5xZ2xZ2xZ2xZ2xZ2
     
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