A characterization of the artin–mumford curve

Let M be the Artin-Mumford curve over the finite prime field F-p with p > 2. By a result of Valentini and Madan, Aut(Fp) (M) congruent to H with H = (C-p x C-p) x Dp-1 We prove that if X is an algebraic curve of genus g = (p - 1)(2) defined over F-p such that Aut(Fp) (X) contains a subgroup isomorphic to H then X is birationally equivalent over F-p to the Artin Mumford curve M154278291FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP2014/03497-