Lifting map automorphisms and MacBeath's theorem

AbstractThe purpose of the present note is essentially twofold. First we indicate how coverings of maps can be obtained easily and in a direct way by using a cohomological construction. Second, we apply this construction to obtain in an explicit way infinitely many examples of finite maps which are extremal in the sense of having 84(g − 1) automorphisms, where g is the genus of the map. This latter result is MacBeath's theorem of the title