Unramified Galois Coverings of Algebraic Curves Original Research Article

Let X be a complete irreducible nonsingular algebraic curve defined over an algebraically closed field k of characteristic p. We consider a finite group G of order prime to p. In this paper we count the number of unramified Galois coverings of X whose Galois group is isomorphic to an extension of G by a finite group which is an irreducible imagep[G]-module. In this counting we use Rück′s definition of generalized Hasse-Witt invariants, obtaining a generalization of results of Nakajima and Katsurada.