Original scientific paper

https://doi.org/10.3336/gm.49.2.08

On finite index subgroups of the mapping class group of a nonorientable surface

Błażej Szepietowski orcid.org/0000-0002-6219-7895 ; Institute of Mathematics, Gdansk University, Wita Stwosza 57, 80-952 Gdansk, Poland

Abstract

Let M(Nh,n) denote the mapping class group of a compact nonorientable surface of genus h ≥ 7 and n ≤ 1 boundary components, and let T(Nh,n) be the subgroup of M(Nh,n) generated by all Dehn twists. It is known that T(Nh,n) is the unique subgroup of M(Nh,n) of index 2. We prove that T(Nh,n) (and also M(Nh,n)) contains a unique subgroup of index 2g-1(2g-1) up to conjugation, and a unique subgroup of index 2g-1(2g+1) up to conjugation, where g = ⌊(h-1)/2⌋. The other proper subgroups of T(Nh,n) and M(Nh,n) have index greater than 2g-1(2g+1). In particular, the minimum index of a proper subgroup of T(Nh,n) is 2g-1(2g-1).

Keywords

Mapping class group; nonorinatble surface; finite index subgroup

Hrčak ID:

130888

URI

https://hrcak.srce.hr/130888

Publication date:

18.12.2014.

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