17.25 (2010)
Open(S. P. Farbman). Let $X$ be the set of complex numbers $\alpha$ such that the group generated by the two $2 \times 2$ matrices $I + \alpha e_{12}$ and $I + e_{21}$ is not free on those generators.
$\qquad$ a) Does $X$ contain all rational numbers in the interval $(-4, 4)$?
$\qquad$ b) Does $X$ contain any rational number in the interval $[27/7, 4)$?
Cf. 4.41, 15.83, and (S. P. Farbman, Publ. Mat., 39 (1995) 379–391).
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