(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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??

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Transpositions in algebra

**Physics Forums | Science Articles, Homework Help, Discussion**