### Abstract

Original language | English |
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Pages (from-to) | 54-57 |

Number of pages | 4 |

Journal | Lecture Notes in Computer Science |

Volume | 6327 |

DOIs | |

Publication status | Published - 2010 |

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

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### Cite this

*Lecture Notes in Computer Science*,

*6327*, 54-57. https://doi.org/10.1007/978-3-642-15582-6_11

}

*Lecture Notes in Computer Science*, vol. 6327, pp. 54-57. 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: Contribution to journal › Conference article

TY - JOUR

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 article

VL - 6327

SP - 54

EP - 57

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -