An elementary abelian \(p\)-cover of the Hermitian curve with many automorphisms (Q2172486)

The authors determine the full automorphism group of a certain elementary abelian \(p\)-cover of the Hermitian curve in characteristic \(p>0\) whose plane model belongs to a family of plane curves with two Galois points, as introduced by the second author in [\textit{S. Fukasawa}, in: Contemporary developments in finite fields and applications. Hackensack, NJ: World Scientific. 62--73 (2016; Zbl 1402.11094)]. Furthermore, Weierstrass points, Galois points, Frobenius nonclassicality, and arc property are here investigated. Finally, it is worth mentioning that the order of Sylow \(p\)-groups of the automorphism group is close to Nakajima's bound in terms of the \(p\)-rank.