### Abstract

The paper shows that for every positive integer p > 2, there exists a compact non-orientable surface of genus p with at least 4p automorphisms if p is odd, or at least 8 (p - 2) automorphisms if p is even, with improvements for odd p ≢ 3 mod 12. Further, these bounds are shown to be sharp (in that no larger group of automorphisms exists with genus p) for infinitely many values of p in each congruence class modulo 12, with the possible (but unlikely) exception of 3 mod 12.

Original language | English (US) |
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Pages (from-to) | 65-82 |

Number of pages | 18 |

Journal | Journal of the London Mathematical Society |

Volume | 68 |

Issue number | 1 |

DOIs | |

State | Published - Aug 2003 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Conder, M., Maclachlan, C., Todorovic Vasiljevic, S., & Wilson, S. (2003). Bounds for the number of automorphisms of a compact non-orientable surface.

*Journal of the London Mathematical Society*,*68*(1), 65-82. https://doi.org/10.1112/S0024610703004277