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This is an exercise from a book from Serre called Trees. Given the group

G = < a, b, c | bab

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.

G = < a, b, c | bab

^{−1}= a^{2}, cbc^{−1}= b^{2}, aca^{−1}= c^{2}>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.
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