Translator Disclaimer
July 2020 The torsion generating set of the mapping class groups and the Dehn twist subgroups of non-orientable surfaces of odd genus
Xiaoming Du
Hiroshima Math. J. 50(2): 199-206 (July 2020). DOI: 10.32917/hmj/1595901627

Abstract

Let $N_g$ be the non-orientable surface of genus $g$, $\mathrm{MCG}(N_g)$ the mapping class group of $N_g$, $\mathscr{T} (N_g)$ the index $2$ subgroup generated by all Dehn twists of $\mathrm{MCG}(N_g)$. We prove that for odd genus, $(1)$ if $g = 4k + 3 (k\ge1), \mathrm{MCG}(N_g)$ can be generated by three elements of finite order; $(2)$ if $g = 4k + 1 (k\ge2)$, $\mathscr{T} (N_g)$ can be generated by three elements of finite order.

Citation

Download Citation

Xiaoming Du. "The torsion generating set of the mapping class groups and the Dehn twist subgroups of non-orientable surfaces of odd genus." Hiroshima Math. J. 50 (2) 199 - 206, July 2020. https://doi.org/10.32917/hmj/1595901627

Information

Received: 19 November 2018; Revised: 1 February 2020; Published: July 2020
First available in Project Euclid: 28 July 2020

zbMATH: 07256504
MathSciNet: MR4132588
Digital Object Identifier: 10.32917/hmj/1595901627

Subjects:
Primary: 20F38, 57M20, 57N05

Rights: Copyright © 2020 Hiroshima University, Mathematics Program

JOURNAL ARTICLE
8 PAGES


SHARE
Vol.50 • No. 2 • July 2020
Back to Top