ABELIAN p-GROUPS OF SYMMETRIES OF SURFACES

TALU E. Y.

TAIWANESE JOURNAL OF MATHEMATICS, cilt.15, sa.3, ss.1129-1140, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 3
  • Basım Tarihi: 2011
  • Doi Numarası: 10.11650/twjm/1500406290
  • Dergi Adı: TAIWANESE JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1129-1140
  • Anahtar Kelimeler: Genus spectrum, Minimum reduced stable genus, Symmetries of surfaces
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.