Why is the Braid Group Infinite?

[gioialorusso]

Hi,
can anyone explain me why (mathematically) the braid group is infinte? I guess it's infinite because you can do every braid you want and even if you braid two particles interchanging them twice in a clock (or counterclock) wise manner, (so you bring them back at the original positions), the system does not necessarily back to the same state. But has someone a good explanation of this fact?
Thank you,
gioia

 

[martinbn]

B_1 is trivial, B_2 is infinite cyclic and B_{n-1} is a subgroup of B_n, so from the second on they are infinite.