# Cyclic group of permutations. f_n(x) = x + n

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• Oct 20th 2012, 04:38 PM
pirateboy
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 $\displaystyle f_n$ has an inverse, $\displaystyle f^{-1} = f_{-n}$
• Oct 20th 2012, 04:42 PM
ILikeSerena
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...?
• Oct 20th 2012, 05:16 PM
pirateboy
Re: Cyclic group of permutations. f_n(x) = x + n
Errr. Rather The group is, please correct my notation here. is $\displaystyle \left< x + n\mathbb{Z}\right>$

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.
• Oct 20th 2012, 05:22 PM
ILikeSerena
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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