Algebraic curves admitting inner and outer Galois points

Abstract

There are two purposes in this article. One is to present a criterion for the existence of a birational embedding into a projective plane with inner and outer Galois points for algebraic curves. Another is to classify plane curves of degree $d$ admitting an inner Galois point $P$ and an outer Galois point $Q$ with $G_P{G}_Q=G_P⋊G_Q$ or $G_P⋉G_Q$, under the assumption that the characteristic $p$ is zero or $p$ does not divide $d-1$.

15 pages