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Math Help - |<a>| = |a|

  1. #1
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    |<a>| = |a|

    how to prove this:

    Let G be a group and a e G an element of finite order. Then |<a>| = |a|.


    Thank you!! ;]
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  2. #2
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    Prove that <a>= \{a, a^2, a^3, \cdot\cdot\cdot, a^{|a|- 1}, e\} where "e" is the group identity.
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  3. #3
    MHF Contributor Swlabr's Avatar
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    EDIT: apparently, it took me 5 minutes to reply to this. HallsofIvy's way is better than mine, methinks...
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  4. #4
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    I am not so sure of the proof i have. Can please show me? I am not that good in proving.
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  5. #5
    MHF Contributor Swlabr's Avatar
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    Well, what have you written so far?
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  6. #6
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    A proof on the corollary of the Lagrange's Theorem. It's |a| divides |G|. I just stated there that a part of the proof for the corollary is to note/recall that |<a>| = |a|. And i think i also have to show the proof for |<a>| = |a|, because maybe my classmates might ask. ;]
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  7. #7
    MHF Contributor Swlabr's Avatar
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    Yes, but what have you written with respect to this problem? Have you looked at what HallsofIvy suggested?
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  8. #8
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    Im really not good in proving.
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  9. #9
    MHF Contributor Swlabr's Avatar
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    Yes, but you have to at least try! We're not here to do your work for you, but to help you with it. This involves, well, you doing some work...
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