# Conjugation of a permutation by a permutation in a permutation group

1. Feb 17, 2008

### karnten07

1. The problem statement, all variables and given/known data
Let n $$\geq$$1. Let <a1,...,as> $$\in$$Sn be a cycle and let $$\sigma$$$$\in$$Sn 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?

2. Feb 17, 2008

### morphism

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

3. Feb 18, 2008

### karnten07

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)).