### Abstract

Original language | English |
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Title of host publication | Mathematical Software – ICMS 2010 |

Subtitle of host publication | Third International Congress on Mathematical Software, Kobe, Japan, September 13-17, 2010. Proceedings |

Editors | Komei Fukuda, Joris van der Hoeven, Michael Joswig, Nobuki Takayama |

Place of Publication | Heidelberg, Germany |

Pages | 54-57 |

Number of pages | 4 |

Volume | 6327 |

ISBN (Electronic) | 978-3-642-15582-6 |

DOIs | |

Publication status | Published - 2010 |

Event | International Congress on Mathematical Software ICMS2010 - Kobe, Kobe, Japan Duration: 13 Sep 2010 → 17 Sep 2010 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | International Congress on Mathematical Software ICMS2010 |
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Abbreviated title | ICMS2010 |

Country | Japan |

City | Kobe |

Period | 13/09/10 → 17/09/10 |

### Fingerprint

### Cite this

*Mathematical Software – ICMS 2010: Third International Congress on Mathematical Software, Kobe, Japan, September 13-17, 2010. Proceedings*(Vol. 6327, pp. 54-57). (Lecture Notes in Computer Science). Heidelberg, Germany. https://doi.org/10.1007/978-3-642-15582-6_11

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*Mathematical Software – ICMS 2010: Third International Congress on Mathematical Software, Kobe, Japan, September 13-17, 2010. Proceedings.*vol. 6327, Lecture Notes in Computer Science, Heidelberg, Germany, pp. 54-57, International Congress on Mathematical Software ICMS2010, Kobe, Japan, 13/09/10. https://doi.org/10.1007/978-3-642-15582-6_11

**Constructive Membership Testing in Black-Box Classical Groups.** / Ambrose, Sophie; Murray, Scott; Praeger, Cheryl; Schneider, Csaba.

Research output: A Conference proceeding or a Chapter in Book › Conference contribution

TY - GEN

T1 - Constructive Membership Testing in Black-Box Classical Groups

AU - Ambrose, Sophie

AU - Murray, Scott

AU - Praeger, Cheryl

AU - Schneider, Csaba

PY - 2010

Y1 - 2010

N2 - The research described in this note aims at solving the constructive membership problem for the class of quasisimple classical groups. Our algorithms are developed in the black-box group model (see [HCGT, Section 3.1.4]); that is, they do not require specific characteristics of the representations in which the input groups are given. The elements of a black-box group are represented, not necessarily uniquely, as bit strings of uniform length. We assume the existence of oracles to compute the product of two elements, the inverse of an element, and to test if two strings represent the same element. Solving the constructive membership problem for a black-box group G requires to write every element of G as a word in a given generating set. In practice we write the elements of G as straight-line programs (SLPs) which can be viewed as a compact way of writing words; see [HCGT, Section 3.1.3]

AB - The research described in this note aims at solving the constructive membership problem for the class of quasisimple classical groups. Our algorithms are developed in the black-box group model (see [HCGT, Section 3.1.4]); that is, they do not require specific characteristics of the representations in which the input groups are given. The elements of a black-box group are represented, not necessarily uniquely, as bit strings of uniform length. We assume the existence of oracles to compute the product of two elements, the inverse of an element, and to test if two strings represent the same element. Solving the constructive membership problem for a black-box group G requires to write every element of G as a word in a given generating set. In practice we write the elements of G as straight-line programs (SLPs) which can be viewed as a compact way of writing words; see [HCGT, Section 3.1.3]

U2 - 10.1007/978-3-642-15582-6_11

DO - 10.1007/978-3-642-15582-6_11

M3 - Conference contribution

SN - 978-3-642-15581-9

VL - 6327

T3 - Lecture Notes in Computer Science

SP - 54

EP - 57

BT - Mathematical Software – ICMS 2010

A2 - Fukuda, Komei

A2 - van der Hoeven, Joris

A2 - Joswig, Michael

A2 - Takayama, Nobuki

CY - Heidelberg, Germany

ER -