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
Solution:
We know that is the subset of even permutations in .
is product of odd number of transpositions in ; permutation in is product of even number of transpositions in .
So, result of product of and permutation in is:
(odd number of transpositions in )+(even number of transpositions in )
=(odd number of transpositions in )
=odd permutation in .
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