### Abstract

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 |

### Fingerprint

### Cite this

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

**Torsion in maximal arithmetic Fuchsian groups.** / MacLachlan, Colin.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Combinatorial Group Theory, Discrete Groups, and Number Theory.*vol. 421, Contemporary Mathematics, vol. 421, American Mathematical Society, Providence, RI, USA, pp. 213-225, ASM Special Meeting on Infinite Group Theory , New York, United States, 8/10/05.

}

TY - CHAP

T1 - Torsion in maximal arithmetic Fuchsian groups

AU - MacLachlan, Colin

PY - 2007/1/18

Y1 - 2007/1/18

N2 - 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.

AB - 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.

M3 - Chapter

SN - 0821839853

SN - 978-0821839850

VL - 421

T3 - Contemporary Mathematics

SP - 213

EP - 225

BT - Combinatorial Group Theory, Discrete Groups, and Number Theory

PB - American Mathematical Society

CY - Providence, RI, USA

ER -