A Note on Nonresidually Solvable Hyperlinear One-Relator Groups

We prove that various non-residually nite, non-residually solvable groups of the form ha; bjrrw = ri are so c. This paper concerns the so c property discussed in the survey [Pest08]. Particularly, we address Question 4.10 in this paper: the problem of Nate Brown asking whether or not every one relator group is so c. In [Ban10], the rst author proves that the example in [Baum69] of a non-residually nite non-residually solvable one relator group is a so c group. The purpose of this paper is to exhibit more such examples in the following large class of non-residually solvable one-relator groups introduced in [BaMiTro07]. Let F2 = ha; bj i denote the free group on two generators. Let r; w 2 F2 be two elements that do not commute. In [BaMiTro07], the authors show that the group r;w = ha; bjr w = ri = ha; bjr = [r; (r )]i has the same nite quotients as the group