Erratum to Right orderable groups that are not locally indicable, Pacific J. Math., 147 (1991) 243-248.
In section 6, I mention that the perfect group  ⟨x, y, z | x2 = y3 = z7 = xyz ⟩  was already known to topologists to be right orderable, and I describe it as the subgroup of the group  G  considered in the paper generated by appropriate  xy  and  z.  It is easy to verify that those elements of  G  satisfy the stated relations, so the subgroup they generate is certainly a homomorphic image of the group with the above presentation; but I failed to give any reason why it could not be a proper homomorphic image. 

In each of the two groups, the common value of  x2 = y3 = z7 = xyz  generates an infinite cyclic central subgroup; so it suffices to show that the homomorphism between the factor-groups by this subgroup is an isomorphism; i.e., between  ⟨x, y, z | x2 = y3 = z7 = xyz = 1⟩  and its image in  PSL(2, R).  The former group, I have learned, is denoted  D(2,3,7).   The groups  D(l,m,n)  with general exponents  l, m, n,  in place of  2, 3, 7  are called von Dyck groups (or simply Dyck groups); and the von Dyck groups  D(2,m,n)  have natural descriptions as symmetry groups of tesselations.  In particular,  D(2,3,7)  is the group of proper symmetries of the tesselation of the hyperbolic plane by 7-gons meeting 3 at a vertex [12, section 5.3].  I am told that isometries of the hyperbolic plane can be represented by 2×2 matrices, and that this leads to the desired isomorphism between  D(2,3,7)  and the desired subgroup of  PSL(2, R),  but I do not at this time know references for the relevant facts. 

[12] H. S. M. Coxeter and W. O. J. Moser, Generators and relations for discrete groups, Springer-Verlag, 1957, 1965, 1972, 1980.

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