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Hi!

There's a theorem 7.43 in p.221(Hungerford's abstract algebra) which states that every permutation in S[itex]_{n}[/itex] is a product of transpositions.

What I know about the concept of transposition is it is defined if there are at least two distinct elements. But, in the above theorem, there's no assumption to prevent that n could be 1. I think, in that case, saying a product of transpositions is meaningless.

So, I think an assumption such as n[itex]\geq[/itex]2 must be added in the above theorem.

Am I wrong?? If so, could you explain why??

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# Homework Help: Transpositions in algebra

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