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Math Help - Cyclic group of permutations. f_n(x) = x + n

  1. #16
    Junior Member pirateboy's Avatar
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    Re: Cyclic group of permutations. f_n(x) = x + n

    I can generate the sum of all integers and x. I meant to show that f_n has an inverse, f^{-1} = f_{-n}
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  2. #17
    Super Member ILikeSerena's Avatar
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    Re: Cyclic group of permutations. f_n(x) = x + n

    Hmm, if I compose fn and fn, I get f2n.

    You did not really say what n is yet.
    Suppose I pick n=3.
    Then I have f3, f6, f9, ...
    Not sure if I get all elements then...?
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  3. #18
    Junior Member pirateboy's Avatar
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    Re: Cyclic group of permutations. f_n(x) = x + n

    Errr. Rather The group is, please correct my notation here. is \left< x + n\mathbb{Z}\right>

    The generator would be x + n?

    That is for all x in reals, for some integer n, I can generate sum of x and all integer multiples of n.
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  4. #19
    Super Member ILikeSerena's Avatar
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    Re: Cyclic group of permutations. f_n(x) = x + n

    That would be correct.
    The notation would be <fn> which would have the generator fn.

    However, the problem statement does not mention that cyclic group, does it?

    Perhaps you can pick a specific n?
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