Give a two-sentence synopsis of Proof 2 of Theorem 9.15. Data from 9.15 Theorem No permutation in

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Give a two-sentence synopsis of Proof 2 of Theorem 9.15.

Data from 9.15 Theorem

No permutation in S_n can be expressed both as a product of an even number of transpositions and as a product of an odd number of transposition.

Proof 2 of 9.15 Theorem

Let a ∈ S_n and let r = (i, j) be a transposition in S_n. We claim that the number of orbits of σ and of r σ differ by 1.

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A First Course In Abstract Algebra

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Give a two-sentence synopsis of Proof 2 of Theorem 9.15. Data from 9.15 Theorem No permutation in

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If is a permutation and i j is a transposition in S n then by considering whether i a...View the full answer

A First Course In Abstract Algebra

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