The finitary andrews-curtis conjecture

Alexandre V. Borovik; Alexander Lubotzky; Alexei G. Myasnikov

doi:10.1007/3-7643-7447-0_2

The finitary andrews-curtis conjecture

Alexandre V. Borovik, Alexander Lubotzky, Alexei G. Myasnikov

Einstein Institute of Mathematics

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

9 Scopus citations

Abstract

The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent importance for computational group theory. It also resolves a question asked in [5] and shows that a computation in finite groups cannot lead to a counterexample to the classical conjecture, as suggested in [5].

Original language	English
Title of host publication	Progress in Mathematics
Publisher	Springer Basel
Pages	15-30
Number of pages	16
DOIs	https://doi.org/10.1007/3-7643-7447-0_2
State	Published - 2005

Publication series

Name	Progress in Mathematics
Volume	248
ISSN (Print)	0743-1643
ISSN (Electronic)	2296-505X

Bibliographical note

Publisher Copyright:
© 2005, Birkhäuser Verlag Basel/Switzerland.

Keywords

Andrews-Curtis conjecture
Finite group
Generators

Access to Document

10.1007/3-7643-7447-0_2

Cite this

@inbook{435f64577c2a456b90cf731d11a69c4a,

title = "The finitary andrews-curtis conjecture",

abstract = "The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent importance for computational group theory. It also resolves a question asked in [5] and shows that a computation in finite groups cannot lead to a counterexample to the classical conjecture, as suggested in [5].",

keywords = "Andrews-Curtis conjecture, Finite group, Generators",

author = "Borovik, \{Alexandre V.\} and Alexander Lubotzky and Myasnikov, \{Alexei G.\}",

note = "Publisher Copyright: {\textcopyright} 2005, Birkh{\"a}user Verlag Basel/Switzerland.",

year = "2005",

doi = "10.1007/3-7643-7447-0\_2",

language = "אנגלית",

series = "Progress in Mathematics",

publisher = "Springer Basel",

pages = "15--30",

booktitle = "Progress in Mathematics",

}

TY - CHAP

T1 - The finitary andrews-curtis conjecture

AU - Borovik, Alexandre V.

AU - Lubotzky, Alexander

AU - Myasnikov, Alexei G.

PY - 2005

Y1 - 2005

N2 - The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent importance for computational group theory. It also resolves a question asked in [5] and shows that a computation in finite groups cannot lead to a counterexample to the classical conjecture, as suggested in [5].

AB - The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent importance for computational group theory. It also resolves a question asked in [5] and shows that a computation in finite groups cannot lead to a counterexample to the classical conjecture, as suggested in [5].

KW - Andrews-Curtis conjecture

KW - Finite group

KW - Generators

UR - https://www.scopus.com/pages/publications/84954310977

U2 - 10.1007/3-7643-7447-0_2

DO - 10.1007/3-7643-7447-0_2

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.chapter???

AN - SCOPUS:84954310977

T3 - Progress in Mathematics

SP - 15

EP - 30

BT - Progress in Mathematics

PB - Springer Basel

ER -

The finitary andrews-curtis conjecture

Abstract

Publication series

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this