Thread: Help with proof: If a is in S_n and commutes with every b in S_n, then a=(1)

Prove that for n>=3, if a is in S_n and commutes with every b in S_n,
then a=(1)

?

Are matrix ?

Originally Posted by math2009

?

Are matrix ?

No a and b are permutations in S_n.

S_n being the symmetric group on n letters.

Originally Posted by didact273

Prove that for n>=3, if a is in S_n and commutes with every b in S_n, then a=(1)

let so there exist with since there exists such that

now let then thus