ABELIAN p-GROUPS OF SYMMETRIES OF SURFACES

TALU E. Y.

TAIWANESE JOURNAL OF MATHEMATICS, vol.15, no.3, pp.1129-1140, 2011 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 3
  • Publication Date: 2011
  • Doi Number: 10.11650/twjm/1500406290
  • Journal Name: TAIWANESE JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1129-1140
  • Keywords: Genus spectrum, Minimum reduced stable genus, Symmetries of surfaces
  • Middle East Technical University Affiliated: Yes

Abstract

An integer g >= 2 is said to be a genus of a finite group G if there is a compact Riemann surface of genus g on which G acts as a group of automorphisms. In this paper finite abelian p-groups of arbitrarily large rank, where p is an odd prime, are investigated. For certain classes of abelian p-groups the minimum reduced stable genus sigma(0) of G is calculated and consequently the genus spectrum of G is completely determined for certain "extremal" abelian p-groups. Moreover for the case of Z(p)(r1) circle plus Z(p2)(r2) we will see that the genus spectrum determines the isomorphism class of the group uniquely.