@entry{ent-pir-22-aa, author = {A Entin and N Pirani}, title = {Abhyankar's Affine Arithmetic Conjecture for the Symmetric and Alternating Groups}, journal = {arXiv preprint arXiv:2205.03879,}, year = 2022, url = {{\url{https://arxiv.org/abs/2205.03879}}}, quotes = {We prove that for any prime $p>2$, $q=p^\nu$ a power of $p$, $n\ge p$ and $G=S_n$ or $G=A_n$ (symmetric or alternating group) there exists a Galois extension $K/\mathbb F_q(T)$ ...} }