Results 1 to 2 of 2

Math Help - Order of abelian groups

  1. #1
    Junior Member
    Joined
    Mar 2008
    Posts
    33

    Order of abelian groups

    I have difficulty to do the following question,

    (a)Determine (up to isomorphism) all abelian groups of order 120.
    My answer:
    C_2 \times C_2 \times C_2 \times C_3 \times C_5
    C_2 \times C_4 \times C_3 \times C_5
    C_8 \times C_3 \times C_5

    (b)Verify that Z_{20} \times Z_{24}/<(5,6)> is an abelian group of order 120. To which of the groups listed in part (a) is isomorphic?

    Part (a) should be correct but I don't know how to do (b). Please help me, thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by kleenex View Post
    (b)Verify that Z_{20} \times Z_{24}/<(5,6)> is an abelian group of order 120. To which of the groups listed in part (a) is isomorphic?
    Hint: (G_1\times G_2)/(H_1\times H_2) \simeq (G_1/H_1)\times (G_2/H_2).
    Where H_1,H_2 are normal subgroups.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Classification of Non-Abelian Groups of Order 42
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: August 24th 2011, 09:01 PM
  2. How Many Abelian Groups of Given Order
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 31st 2011, 05:27 PM
  3. Abelian groups and Homology groups
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: December 6th 2010, 02:44 PM
  4. Non-abelian groups of order p^2 q
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: June 16th 2009, 01:32 AM
  5. Order of groups involving conjugates and abelian groups
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: February 5th 2009, 09:55 PM

Search Tags


/mathhelpforum @mathhelpforum