Generating the Mapping Class Group by Two Torsion Elements

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Yildiz O.

MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.19, sa.2, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s00009-022-01978-8
  • Dergi Adı: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We prove that the mapping class group of a closed connected orientable surface of genus g >= 6 is generated by two elements of order g. Moreover, for g >= 7, we obtain a generating set of two elements, of order g and g', where g' is the least divisor of g greater than 2. We also prove that the mapping class group is generated by two elements of order g/gcd(g, k) for g >= 3k(2) + 4k + 1 and any positive integer k.