### Abstract

In this paper, formulas are derived for the number of conjugacy classes of finite cyclic subgroups in a family of arithmetic Fuchsian groups which includes all maximal arithmetic Fuchsian groups. These formulas are given in terms of the arithmetic data which defines the group. Since a formula for the co-area of these groups in similar terms is also known, this means that the signature and hence isomorphism class of any maximal arithmetic Fuchsian group can be completely determined from the arithmetic data defining the group.

Original language | English |
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Title of host publication | Combinatorial Group Theory, Discrete Groups, and Number Theory |

Place of Publication | Providence, RI, USA |

Publisher | American Mathematical Society |

Pages | 213-225 |

Number of pages | 13 |

Volume | 421 |

ISBN (Print) | 0821839853, 978-0821839850 |

Publication status | Published - 18 Jan 2007 |

Event | ASM Special Meeting on Infinite Group Theory - New York, United States Duration: 8 Oct 2005 → 9 Oct 2005 |

### Publication series

Name | Contemporary Mathematics |
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Publisher | American Mathematical Society |

Volume | 421 |

ISSN (Print) | 0271-4132 |

### Conference

Conference | ASM Special Meeting on Infinite Group Theory |
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Country | United States |

City | New York |

Period | 8/10/05 → 9/10/05 |

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## Cite this

MacLachlan, C. (2007). Torsion in maximal arithmetic Fuchsian groups. In

*Combinatorial Group Theory, Discrete Groups, and Number Theory*(Vol. 421, pp. 213-225). (Contemporary Mathematics; Vol. 421). American Mathematical Society.