Consider the permutation ρ = (1, 2, 6)(3, 4, 5) in S10. How many conjugates does...

Consider the permutation ρ = (1, 2, 6)(3, 4, 5) in S10. How many conjugates does ρ has in S10? Hence determine the order of Cρ(S10), the centralizer of ρ in S10. Now determine the order of Cρ(A10) by observing that there is an odd permutation in Cρ(S10). How many conjugates does ρ has as an element of A10?

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Colby Messinger answered 3 months ago

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