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banana112
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Homework Statement
What subgroup is generated by the fixed-point-free permutations?
Homework Equations
The Attempt at a Solution
I know that the elements that have no fixed points are the ones whose cycle type adds up to n (i.e. all the numbers in {1,...,n} have to be used). I don't know what to do other than just start computing examples and multiplying out every single combination. EDIT I think they generate all of Sn. I know this is true up to 5, and whenever we have n odd. (We can generate the transpositions, which in turn generate all of Sn.) For odd n this works by: (1,2)=[(1,2)(3,4,...,n)]^(n-2). I haven't yet found something similar for the case when n is even.
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