Reference : From the Poincaré theorem to generators of the unit group of integral group rings of ... |

Scientific journals : Article | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/45741 | |||

From the Poincaré theorem to generators of the unit group of integral group rings of finite groups | |

English | |

Jespers, E. [> >] | |

Juriaans, S. O. [> >] | |

Kiefer, Ann [University of Luxembourg > Faculty of Humanities, Education and Social Sciences (FHSE) > LUCET] | |

de A. e Silva, A. [> >] | |

Souza Filho, A. C. [> >] | |

2015 | |

Mathematics of Computation | |

84 | |

293 | |

1489--1520 | |

Yes (verified by ORBi^{lu}) | |

0025-5718 | |

1088-6842 | |

[en] Units ; Group Rings ; Fundamental Domain ; Generator | |

[en] We give an algorithm to determine finitely many generators for a subgroup of finite index
in the unit group of an integral group ring ZG of a finite nilpotent group G, this provided the rational group algebra QG does not have simple components that are division classical quaternion algebras or two-by-two matrices over a classical quaternion algebra with centre Q. The main difficulty is to deal with orders in quaternion algebras over the rationals or a quadratic imaginary extension of the rationals. In order to deal with these we give a finite and easy implementable algorithm to compute a fundamental domain in the hyperbolic three space H 3 (respectively hyperbolic two space H 2 ) for a discrete subgroup of PSL 2 (C) (respectively PSL 2 (R)) of finite covolume. Our results on group rings are a continuation of earlier work of Ritter and Sehgal, Jespers and Leal. | |

http://hdl.handle.net/10993/45741 | |

10.1090/S0025-5718-2014-02865-2 | |

http://dx.doi.org/10.1090/S0025-5718-2014-02865-2 |

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