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Ultraworld
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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: I am going to try to use Todd Coxeter coset enumeration.
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: I am going to try to use Todd Coxeter coset enumeration.
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