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16.101 (2006)

Solved

Do there exist uncountably many infinite 2-groups that are quotients of the group $\langle x, y \mid x^2 = y^4 = (xy)^8 = 1 \rangle$? There certainly exists one, namely the subgroup of finite index in Grigorchuk's first group generated by $b$ and $ad$; see (R. I. Grigorchuk, Functional Anal. Appl., 14 (1980), 41–43).

Contributor: J. Wiegold

Progress

Yes, there do (R. I. Grigorchuk, Algebra Discrete Math., 2009, no. 4 (2009), 78–96 (subm. 25 November 2009); A. Minasyan, A. Yu. Olshanskii, D. Sonkin, Groups Geom. Dynam., 3, no. 3 (2009) 423–452 (subm. 21 April 2008)).

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