This is an exercise from a book from Serre called Trees. Given the group G = < a, b, c | bab−1 = a2, cbc−1 = b2, aca−1 = c2 > I have to prove G = 1. I don't have a clue. Of course G' = G (commutator subgroup equals the group itself) but I don't know what to deduce from that. Another first step could be to prove that the orders of a, b and c are finite. But I do not even know how to that. If anyone could put me in the right direction i would be very grateful. edit: Im gonna try to use Todd Coxeter coset enumeration.