CONJUGACY CLASSES OF AUTOMORPHISMS p-GROUPS

Abstract

Abstract. In this paper we provide examples of pairs of conformallynon-equivalent, but topologically equivalent, p -groups H 1 ;H 2 < Aut( S ),where S is a closed Riemann surface of genus g  2, so that S=H j hasgenus zero and all its cone points are of order equal to p . 1. IntroductionWe denote by Aut( S ) the group of conformal automorphisms of a Riemannsurface S . If S 1 and S 2 are Riemann surfaces, then we say that H 1 < Aut( S 1 )and H 2 < Aut( S 2 ) are topologically equivalent (respectively, conformally equiv-alent ) if there is an orientation preserving homeomorphism (respectively, aconformal homeomorphism) f : S 1 ! S 2 so that H 2 = fH 1 f 1 . In this paper,we assume S 1 = S 2 . Sources for the matter of characterization of topologi-cal conjugacy for surface automorphisms by certain purely algebraic data areJ. Nielsen [14], W. J. Harvey [12], and J. Gilmann [9]. In general, it is nothard to construct an example of a closed Riemann surface S , of genus g  2,and pairs