Let S9 be a permutaion group of order 9.then number of element commutate to (1 2 3)(4 5 6 7)
Consider the group S9 of all the permutations on a set with 9 elements. What is the largest order of a permutation in S9?
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$\begingroup$
permutations
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0Is 15120?...plz help me – 2017-02-06
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0Hint: Construct the group generated by $(1,2,3)(4,5,6,7)$ and $(8,9)$. – 2017-02-06
1 Answers
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The set of permutation commutating with x=(1 2 3) (4 5 6 7) in S9 is the centralizer Cs9(x),Therefore [S9 :Cs9(x)]=o(x^S9),the conjugacy class . o(conjugacy class of x in S9)=15120 so o(Cs9(x))=9!/15120=24