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THE TWIST SUBGROUP IS GENERATED BY TWO ELEMENTS
Date
2024-01-01
Author
Altunöz, Tülin
Pamuk, Mehmetcik
Yildiz, Oguz
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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
Journal
Tohoku Mathematical Journal
DOI
https://doi.org/10.2748/tmj.20221017
Collections
Department of Mathematics, Article
Citation Formats
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BibTeX
T. Altunöz, M. Pamuk, and O. Yildiz, “THE TWIST SUBGROUP IS GENERATED BY TWO ELEMENTS,”
Tohoku Mathematical Journal
, vol. 76, no. 2, pp. 175–197, 2024, Accessed: 00, 2024. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85197921265&origin=inward.