The mapping class group is generated by two commutators

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Baykur R. I., KORKMAZ M.

JOURNAL OF ALGEBRA, vol.574, pp.278-291, 2021 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 574
• Publication Date: 2021
• Doi Number: 10.1016/j.jalgebra.2021.01.021
• Journal Name: JOURNAL OF ALGEBRA
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
• Page Numbers: pp.278-291
• Keywords: Mapping class group, Commutators, Generators of a group, Perfect groups, Symplectic group
• Middle East Technical University Affiliated: Yes

Abstract

We show that the mapping class group of any closed connected orientable surface of genus at least five is generated by only two commutators, and if the genus is three or four, by three commutators. (C) 2021 Elsevier Inc. All rights reserved.