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Math Help - Distinct Subgroups

  1. #1
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    Distinct Subgroups

    I am a little confused about distinct subgroups of a group.

    For example ({1,2,4,8,9,13,15,16},x17)

    has the following cyclic groups

    <1> = {1}
    <2> = {1,2,4,8,9,13,15,16}
    <4> = {1,4,13,16}
    <8> = {1,2,4,8,9,13,15,16}
    <9> = {1,2,4,8,9,13,15,16}
    <13> = {1,4,13,16}
    <15> = {1,2,4,8,9,13,15,16}
    <16> = {1,16}

    but what are the distinct subgroups.

    Can anyone help?
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  2. #2
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    Quote Originally Posted by Arron View Post
    I am a little confused about distinct subgroups of a group.

    For example ({1,2,4,8,9,13,15,16},x17)


    I'm afraid you'll have to explain yourself since the above makes no sense.

    Tonio



    has the following cyclic groups

    <1> = {1}
    <2> = {1,2,4,8,9,13,15,16}
    <4> = {1,4,13,16}
    <8> = {1,2,4,8,9,13,15,16}
    <9> = {1,2,4,8,9,13,15,16}
    <13> = {1,4,13,16}
    <15> = {1,2,4,8,9,13,15,16}
    <16> = {1,16}

    but what are the distinct subgroups.

    Can anyone help?
    .
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  3. #3
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    I am talking about the group ({1,2,4,8,9,13,15,16},X 17)

    I'm not sure about its subgroups?
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  4. #4
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    Quote Originally Posted by Arron View Post
    I am talking about the group ({1,2,4,8,9,13,15,16},X 17)

    I'm not sure about its subgroups?


    Once again, what you call "group" has no meaning at all for anyone not knowing your notation, and that is NOT a

    standard notation, so explain what group is that.

    Tonio
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  5. #5
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    Quote Originally Posted by Arron View Post
    I am a little confused about distinct subgroups of a group.

    For example ({1,2,4,8,9,13,15,16},x17)
    I assume you mean that these numbers form a group with the operation being multiplication, modulo 17.

    has the following cyclic groups

    <1> = {1}
    <2> = {1,2,4,8,9,13,15,16}
    <4> = {1,4,13,16}
    <8> = {1,2,4,8,9,13,15,16}
    <9> = {1,2,4,8,9,13,15,16}
    <13> = {1,4,13,16}
    <15> = {1,2,4,8,9,13,15,16}
    <16> = {1,16}

    but what are the distinct subgroups.

    Can anyone help?
    "Distinct" means just that- that the subgroups are "distinct"- different. Of the subgroups you list
    <2>, < 8>, < 9>, and <15> all equal {1,2,4,8,9,13,15,16}
    They are NOT "distinct".

    Also, <4> and <13> both equal {1, 4, 13, 16} so are not distnct.

    counting <1> and <16>, there are 4 "distinct" subgroups- that is, four different subgroups.
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