Generating the Mapping Class Group by Two Torsion Elements


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Yildiz O.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.19, no.2, 2022 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.1007/s00009-022-01978-8
  • Title of Journal : MEDITERRANEAN JOURNAL OF MATHEMATICS

Abstract

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.