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Math Help - Cycle notation...

  1. #1
    Junior Member platinumpimp68plus1's Avatar
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    Cycle notation...

    of permutation groups.

    I'm a little confused as what a question is asking... working in S_5, it says to find a subgroup H that is generated by (123), (23), and (45) (written in cycle notation). Not sure what that means... from what I've learned of cycle notation, i thought (for example) the first would be:
    1->1
    2->2
    3->3
    4->4
    5->5
    and the second:
    1->2
    2->3
    3->??
    4->4
    5->5
    and the third:
    1->4
    2->5
    3->3
    4->1
    5->2

    but then i don't know how to 'generate' a group with these. my understanding is that a generator a produces elements of the subgroup a^2,a^3,...,a^n... but i don't know how to multiply these by themselves to produce new elements.
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  2. #2
    Junior Member platinumpimp68plus1's Avatar
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    i think i might understand now actually. is this correct intepretation of the notation?

    (123)=

    1->2
    2->3
    3->1
    4->4
    5->5

    (23)=
    1->1
    2->3
    3->2
    4->4
    5->5

    (45)=
    1->1
    2->2
    3->3
    4->5
    5->4

    ???
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  3. #3
    Super Member
    Joined
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    Posts
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    Quote Originally Posted by platinumpimp68plus1 View Post
    i think i might understand now actually. is this correct intepretation of the notation?

    (123)=

    1->2
    2->3
    3->1
    4->4
    5->5

    (23)=
    1->1
    2->3
    3->2
    4->4
    5->5

    (45)=
    1->1
    2->2
    3->3
    4->5
    5->4

    ???
    yes
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