The full group of automorphisms of non-orientable unbordered Klein surfaces of topological genus 8

Abstract

It is very difficult to determine the full automorphism group of compact Riemann and Klein surfaces. The automorphism groups of hyperelliptic surfaces, and those of (compact, non-orientable, unbordered) Klein surfaces whose genus is less or equal to 7 are known, but a lot of hard work is left to do. To amplify the knowledge in this field, in this paper the full automorphism groups of the surfaces of genus 8 are calculated.

Keywords:

• Finite groups
• Klein surfaces
• symmetric crosscap number

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 57M60
• Secondary: 20F05
• 20H10
• 30F50

Acknowledgments

I would like to thank the reviewers for their contributions that have improved the article and the professors Javier Etayo, Ernesto Martínez and Jose Luis Estévez for their invaluable help.

Disclosure statement

There is no conflict of interest.

Additional information

Funding

The author is partially supported by UCM910444 and PID2021-122752NB-I00.