# Generating twist subgroup of mapping class group of non-orientable surface by involutions

## TL;DR

This paper proves that the twist subgroup of the mapping class group of a non-orientable surface can be generated by six involutions for certain genera, advancing understanding of the algebraic structure of these groups.

## Contribution

It establishes that the twist subgroup is generated by six involutions for non-orientable surfaces of genus at least 14 or 16, providing a new generating set.

## Key findings

- Twist subgroup generated by six involutions for g ≥ 16 or g = 14
- Improves understanding of algebraic structure of mapping class groups
- Provides explicit generating set for specific genera

## Abstract

Let $N_{g}$ denote the closed non-orientable surface of genus $g$ and let ${\mathcal M} _g$ denote the mapping class group of $N_{g}$. Let ${\mathcal T} _g$ denote the twist subgroup of ${\mathcal M} _g$ which is the subgroup of ${\mathcal M} _g$ is generated by all Dehn twists. In this thesis, we proved that ${\mathcal T} _g$ is generated by six involutions for $g \geq 16$ or $g = 14$.