THE TWIST SUBGROUP IS GENERATED BY TWO ELEMENTS

Date

2024-01-01

Author

Altunöz, Tülin
Pamuk, Mehmetcik
Yildiz, Oguz

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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We show that the twist subgroup Tg of a nonorientable surface of genus g can be generated by two elements for every odd g ≥ 21 and even g ≥ 50. Using these generators, we can also show that Tg can be generated by two or three commutators depending on g modulo 4. Moreover, we show that Tg can be generated by three elements if g ≥ 8. For this general case, the number of commutator generators is either three or four depending on g modulo 4 again.

Subject Keywords

commutators, generating sets, Mapping class groups, nonorientable surfaces, torsion, twist subgroup

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85197921265&origin=inward
https://hdl.handle.net/11511/110272

Collections

Department of Mathematics, Article