The decomposition of primes in nonabelian extensions of Heisenberg type and an analogue of Euler's criterion

Dohyeong Kim, Ingyu Yang

For primes $p$ and $\ell$ such that $\ell$ divides $p-1$, Hirano and Morishita constructed a nonabelian Galois extension of the function field ${\mathbb{F}}_p(t)$ whose degree is $\e…