Answer to Question #196188 in Abstract Algebra for Mohd Arsalan

Question #196188

Let τ be a fixed odd permutation in . S10 Show that every odd permutation in S10 is a product of τ and some permutation in A10


1
Expert's answer
2021-05-21T15:21:01-0400

Solution:

We know that A10A_{10} is the subset of even permutations in S10S_{10}.

τ\tau is product of odd number of transpositions in S10S_{10} ; permutation in A10A_{10} is product of even number of transpositions in S10S_{10} .

So, result of product of τ\tau and permutation in A10A_{10} is:

(odd number of transpositions in S10S_{10} )+(even number of transpositions in S10S_{10} )

=(odd number of transpositions in S10S_{10} )

=odd permutation in S10S_{10}.


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