Re: Generators and relations

since x is not a power of r it will be a multiplication of power of r and s say

$\displaystyle x = r^k s $

we have to show that $\displaystyle r r^k s = r^k s r^{-1} $

Re: Generators and relations

Quote:

Originally Posted by

**Amer** since x is not a power of r it will be a multiplication of power of r and s say

$\displaystyle x = r^k s $

we have to show that $\displaystyle r r^k s = r^k s r^{-1} $

Can I do this:

Since $\displaystyle rs=sr^{-1}$, $\displaystyle r^ksr^{-1}=r^krs=r^{k+1}s\equiv rr^ks=r^{k+1}s$

Re: Generators and relations

Quote:

Originally Posted by

**dwsmith** Can I do this:

Since $\displaystyle rs=sr^{-1}$, $\displaystyle r^ksr^{-1}=r^krs=r^{k+1}s\equiv rr^ks=r^{k+1}s$

Yup, that works.