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

1. ## 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, $f^{-1} = f_{-n}$

2. ## 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...?

3. ## 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.

4. ## 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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