### Abstract

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]

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 |

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## Cite this

Ambrose, S., Murray, S., Praeger, C., & Schneider, C. (2010). Constructive Membership Testing in Black-Box Classical Groups. In K. Fukuda, J. van der Hoeven, M. Joswig, & N. Takayama (Eds.),

*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).. https://doi.org/10.1007/978-3-642-15582-6_11