### 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) |
---|---|

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 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of the London Mathematical Society*,

*68*(1), 65-82. https://doi.org/10.1112/S0024610703004277

**Bounds for the number of automorphisms of a compact non-orientable surface.** / Conder, Marston; Maclachlan, Colin; Todorovic Vasiljevic, Sanja; Wilson, Stephen E.

Research output: Contribution to journal › Article

*Journal of the London Mathematical Society*, vol. 68, no. 1, pp. 65-82. https://doi.org/10.1112/S0024610703004277

}

TY - JOUR

T1 - Bounds for the number of automorphisms of a compact non-orientable surface

AU - Conder, Marston

AU - Maclachlan, Colin

AU - Todorovic Vasiljevic, Sanja

AU - Wilson, Stephen E

PY - 2003/8

Y1 - 2003/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0041860936&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041860936&partnerID=8YFLogxK

U2 - 10.1112/S0024610703004277

DO - 10.1112/S0024610703004277

M3 - Article

VL - 68

SP - 65

EP - 82

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 1

ER -