Conjugation of a permutation by a permutation in a permutation group

[karnten07]

1. The problem statement, all variables and given/known data
Let n \geq1. Let <a1,...,as> \inSn be a cycle and let \sigma\inSn be arbitrary. Show that

\sigma\circ <a1,...,as> \circ\sigma^{-1} = <\sigma(a1),...,\sigma(as)> in Sn.



2. Relevant equations



3. The attempt at a solution
As the title says, i believe this is a theorem regarding that the inverse permutation is the effect of a conjugation of a permutation by a permutation in a permutation group. Does anyone know a proof for this or where to find one?

[morphism]

That's pretty hard to read. It's usually better if you put adjacent things in one [tex] tag instead of several.

[karnten07]

That's pretty hard to read. It's usually better if you put adjacent things in one [tex] tag instead of several.

Im sorry, here it is written in wikipedia simpler:

One theorem regarding the inverse permutation is the effect of a conjugation of a permutation by a permutation in a permutation group. If we have a permutation Q=(i1 i2 … in) and a permutation P, then PQP−1 = (P(i1) P(i2) … P(in)).

Please any help guys

[morphism]

Try it out with specific permutations and see if you can spot a general pattern.