Curves with more than one inner Galois point

Let C be an irreducible plane curve of PG(2, K) where K is an algebraically closed field of characteristic p >= 0. A point Q is an element of C is an inner Galois point for C if the projection pi(Q) from Q is Galois. Assume that C has two different inner Galois points Q(1) and Q(2), both simple. Let G(1) and G(2) be the respective Galois groups. Under the assumption that G(i) fixes Q(i), for = 1, 2, we provide a complete classification of G = < G(1), G(2)> and we exhibit a curve for each such G. Our proof relies on deeper results from group theory. (C) 2020 Elsevier Inc. All rights reserved.