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Jun 7, 2017 at 23:48 comment added YCor For reference: It's also known as "Baumslag-Gersten group". Its soficity follows from stability of soficity under HNN over amenable groups. Cf Remark 2.2 in J. Bannon, A non-residually solvable hyperlinear one-relator group, Proc. Amer. Math. Soc. 139 (2011), 1409-1410, freely accessible: ams.org/journals/proc/2011-139-04/S0002-9939-2010-10668-8
Dec 8, 2010 at 21:30 comment added HJRW Gladly! Unfortunately, I think it's pretty unlikely that I can say anything useful about the modified question.
Dec 8, 2010 at 20:35 comment added Jon Bannon Hi Henry. Sorry about the nonsense! Please have another look.
Dec 8, 2010 at 18:15 comment added HJRW Incidentally, I think the question in the title is still an interesting one.
Dec 8, 2010 at 18:12 history answered HJRW CC BY-SA 2.5