4.41 (1973)
SolvedA point $z$ in the complex plane is called free if the matrices $\begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix}$ and $\begin{pmatrix} 1 & 0 \\ z & 1 \end{pmatrix}$ generate a free group. Are all points outside the rhombus with vertices $\pm 2$, $\pm i$ free?
Progress
No (Yu. A. Ignatov, Math. USSR–Sb., 35 (1979), 49–56; A. I. Shkuratskiĭ, Math. Notes, 24 (1978), 720–721).
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