I'm taking algebraic topology this year and my professor assigned a class an exercise, and he told that the exercise will be on a coming exam.
The exercise is:
Show that $(x,y|xyx=yxy)\cong (a,b|a^2=b^3)$.
I googled it and I found this type of group is called "the Braid group".
How do I show those two presentations are isomorphic?
I asked my professor today that "Do you mean to find an explicit isomorphism between them?". Then, my professor said Yes.
How do I show they are isomorphic?
I have no idea whether there is an relatively easy way to show that..
Please help