Originally Posted by

**alsn** I have the group presentations

$\displaystyle $\left\langle x,y|x^2=1,y^2=1,(xy)^n=1\right\rangle$$

and

$\displaystyle $\left\langle x,y|x^2=1,y^2=1\right\rangle$$

and am told to say what well-known groups they define. I know the second is the infinite dihedral group and so am guessing the first is $\displaystyle $D_n$$, but don't know how to show *why* they are these groups.

Thanks

P.S. in an unrelated question, given a non-abelian group of order 60, how could you show that it has no odd permutations (without using the fact that it is $\displaystyle $A_5$$)?