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Math Help - External Direct Product

  1. #1
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    External Direct Product

    Show that Z_2 + Z_2 + Z_2. has seven subgroups of order 2.

    .How many elements of order 9 does Z_3 + Z_9 have.

    *let all the pluses ('+') represent direct product. (circle plus).
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  2. #2
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    Quote Originally Posted by Juancd08 View Post
    Show that Z_2 + Z_2 + Z_2. has seven subgroups of order 2.
    As as asking how many elements have order 2.
    These are: (1,0,0),(0,1,0),(0,0,1),(1,1,0),(1,0,1),(0,1,1),(1 ,1,1)

    .How many elements of order 9 does Z_3 + Z_9 have.
    Similar to above.
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  3. #3
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    sorry

    Sorry but i cant spell out all the elements. I was told i need to do it a different way. using the thrm that says |(a,b)|=lcm(|a|,|b|).
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