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Math Help - 2-subgroup of Z8

  1. #1
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    2-subgroup of Z8

    Please determine the all 2-subgroups of Z8.
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  2. #2
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    Re: 2-subgroup of Z8

    What have you tried yourself? Can write out the operation table for Z8?
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  3. #3
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    Re: 2-subgroup of Z8

    Quote Originally Posted by seventhson View Post
    Please determine the all 2-subgroups of Z8.
    In fact have solved the question. I just want to check my solution.
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  4. #4
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    Re: 2-subgroup of Z8

    Great! Tell us what your solution is and we will help you check it.
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  5. #5
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    Re: 2-subgroup of Z8

    Quote Originally Posted by HallsofIvy View Post
    Great! Tell us what your solution is and we will help you check it.
    Ok.
    <2> group of order 4
    <3> group of order 8
    <4> group of order 2
    <5> group of order 8
    <6> group of order 4
    <7> group of order 8
    so they are all group of order p^n (n=1,2,3)
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  6. #6
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    Re: 2-subgroup of Z8

    you missed <1> = Z8 (of order 8, of course), and <0>, of order 1.
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