Show that the symmetric group Sn is nonabelian for n geq 3.

sodni3 2021-02-21 Answered

Show that the symmetric group Sn is nonabelian for n3.

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Expert Answer

svartmaleJ
Answered 2021-02-22 Author has 92 answers

Consider first the case where n=3 along with the following transpositions:
ψ=(12) and σ=(23)
Notice that ψ×σ=(123) while σ×ψ=(132), which shows that ψ×σ is not equal to σ×ψ i.e. S3 is not abelian.
Now, these two permuations are in every single symmetric group of order 3. Therefore we must conclude that Sn is not abelian for n3

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