Constructive recognition of classical matrix groups in even characteristic

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

Abstract

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.
Original languageEnglish
Title of host publicationMathematisches Forschungsinstitut Oberwolfach
Subtitle of host publicationReport No. 37/2011 - Computational Group Theory
Place of PublicationGermany
PublisherMathematisches Forschungsinstitut Oberwolfach
Pages2126-2127
Number of pages2
Publication statusPublished - 2011

Cite this

Dietrich, H. (2011). Constructive recognition of classical matrix groups in even characteristic. In Mathematisches Forschungsinstitut Oberwolfach: Report No. 37/2011 - Computational Group Theory (pp. 2126-2127). Germany: Mathematisches Forschungsinstitut Oberwolfach.
Dietrich, Heiko. / Constructive recognition of classical matrix groups in even characteristic. Mathematisches Forschungsinstitut Oberwolfach: Report No. 37/2011 - Computational Group Theory. Germany : Mathematisches Forschungsinstitut Oberwolfach, 2011. pp. 2126-2127
@inproceedings{433fe2ae593c4c95a409304ca6007dd1,
title = "Constructive recognition of classical matrix groups in even characteristic",
abstract = "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.",
author = "Heiko Dietrich",
year = "2011",
language = "English",
pages = "2126--2127",
booktitle = "Mathematisches Forschungsinstitut Oberwolfach",
publisher = "Mathematisches Forschungsinstitut Oberwolfach",

}

Dietrich, H 2011, Constructive recognition of classical matrix groups in even characteristic. in 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.

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

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-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 -

Dietrich H. Constructive recognition of classical matrix groups in even characteristic. In Mathematisches Forschungsinstitut Oberwolfach: Report No. 37/2011 - Computational Group Theory. Germany: Mathematisches Forschungsinstitut Oberwolfach. 2011. p. 2126-2127