# Finite quotients of the algebraic fundamental group of projective curves in positive characteristic

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## Abstract

Let X be a smooth connected projective curve defined over an algebraically closed field k of characteristic p >0. Let G be a finite group whose order is divisible by p. Suppose that G has a normal p-Sylow subgroup. We give a necessary and sufficient condition for G to be a quotient of the algebraic fundamental group pi(1)(X) of X.

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