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Math Help - Order of Hx in Factor Group

  1. #1
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    Order of Hx in Factor Group

    Another Factor Group question

    Question: Let G = U17 and H = <[4]> be the cyclice subgroup generated by [4] in G/H. Find the order of Hx where x = 2 or 3.

    G = {1,2,3,...,16}
    H = {4,8,12,16}
    |G/H| = |G|/|H| = 16/4 = 4
    o(x)|4 (the order of an element must divide the order of the group). so o(x) = 1,2, or 4
    if x = 2 then o(H + [2]) != 1 and 2(H + [2]) = H + [4] = H + [0] so o(H + [2]) = 2
    if x = 3 then o(H+ [3]) != 1 or 2 and 3(H + [3]) = H + [12] = H + [0] so o(H + [3]) = 4

    Thanks in advance!
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  2. #2
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    Quote Originally Posted by temp31415 View Post
    Another Factor Group question

    Question: Let G = U17 and H = <[4]> be the cyclice subgroup generated by [4] in G/H. Find the order of Hx where x = 2 or 3.
    You got it wrong.
    G=\mathbb{Z}_{17}^{\text{x}}=\{1,...,16\}, H=\{4,16,13\}
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  3. #3
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    I think that makes sense. 13 is in H because 64 mod 17 = 13?
    and 1 and 8 aren't in H because they aren't powers of 4?

    Thanks!
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    Remember this is not addition, it is multiplication. Do not get confused.
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