Announcement_2024 04 03

Some collaborators and I have solved an open case of the Inverse Galois Problem! We have realized the transitive group 17T7 as a Galois group over $\mathbb{Q}$. Here’s the polynomial we found: \(\begin{align*} x^{17} &- 2 x^{16} + 12 x^{15} - 28 x^{14} + 60 x^{13} - 160 x^{12} + 200 x^{11} - 500 x^{10} + 705 x^{9} - 886 x^{8}\\ &+ 2024 x^{7} - 604 x^{6} + 2146 x^{5} + 80 x^{4} - 1376 x^{3} - 496 x^{2} - 1013 x - 490 \, . \end{align*}\)