### Abstract

Original language | English |
---|---|

Title of host publication | Mathematisches Forschungsinstitut Oberwolfach |

Subtitle of host publication | Report No. 37/2011 - Computational Group Theory |

Place of Publication | Germany |

Publisher | Mathematisches Forschungsinstitut Oberwolfach |

Pages | 2126-2127 |

Number of pages | 2 |

Publication status | Published - 2011 |

### Cite this

*Mathematisches Forschungsinstitut Oberwolfach: Report No. 37/2011 - Computational Group Theory*(pp. 2126-2127). Germany: Mathematisches Forschungsinstitut Oberwolfach.

}

*Mathematisches Forschungsinstitut Oberwolfach: Report No. 37/2011 - Computational Group Theory.*Mathematisches Forschungsinstitut Oberwolfach, Germany, pp. 2126-2127.

**Constructive recognition of classical matrix groups in even characteristic.** / Dietrich, Heiko.

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

TY - GEN

T1 - Constructive recognition of classical matrix groups in even characteristic

AU - Dietrich, Heiko

PY - 2011

Y1 - 2011

N2 - Let G = hXi be isomorphic to a classical matrix group H = hSi ≤ GL(d, q)in natural representation, where S is a nice generating set. For example, one can efficiently write an arbitrary element of H as a word in S. Informally, a constructive recognition algorithm constructs an effective isomorphism from G to H, and vice versa. An approach for doing this is to consider a generating set S′ ⊆ G corresponding to S, and to write the elements of S′ as words in X. If every element of G can efficiently be written as a word in S′, then the isomorphisms G ↔ H defined by S′ ↔ S are effective since images can be computed readily. For example, if g ∈ G is written as a word w(S′) in S′, then the image of g in H is easily determined as w(S). Thus, instead of working in G, this allows us to work in the nice group H.

AB - Let G = hXi be isomorphic to a classical matrix group H = hSi ≤ GL(d, q)in natural representation, where S is a nice generating set. For example, one can efficiently write an arbitrary element of H as a word in S. Informally, a constructive recognition algorithm constructs an effective isomorphism from G to H, and vice versa. An approach for doing this is to consider a generating set S′ ⊆ G corresponding to S, and to write the elements of S′ as words in X. If every element of G can efficiently be written as a word in S′, then the isomorphisms G ↔ H defined by S′ ↔ S are effective since images can be computed readily. For example, if g ∈ G is written as a word w(S′) in S′, then the image of g in H is easily determined as w(S). Thus, instead of working in G, this allows us to work in the nice group H.

M3 - Conference Paper

SP - 2126

EP - 2127

BT - Mathematisches Forschungsinstitut Oberwolfach

PB - Mathematisches Forschungsinstitut Oberwolfach

CY - Germany

ER -