Standard

Identity with constants in a chevalley group of type f4. / Nesterov, V.; Stepanov, A.

In: St. Petersburg Mathematical Journal, Vol. 21, No. 5, 01.12.2010, p. 819-823.

Research output: Contribution to journal › Article › peer-review

Harvard

Nesterov, V & Stepanov, A 2010, 'Identity with constants in a chevalley group of type f4', St. Petersburg Mathematical Journal, vol. 21, no. 5, pp. 819-823. https://doi.org/10.1090/S1061-0022-2010-01119-1

APA

Nesterov, V., & Stepanov, A. (2010). Identity with constants in a chevalley group of type f4. St. Petersburg Mathematical Journal, 21(5), 819-823. https://doi.org/10.1090/S1061-0022-2010-01119-1

Vancouver

Nesterov V, Stepanov A. Identity with constants in a chevalley group of type f4. St. Petersburg Mathematical Journal. 2010 Dec 1;21(5):819-823. https://doi.org/10.1090/S1061-0022-2010-01119-1

Author

Nesterov, V. ; Stepanov, A. / Identity with constants in a chevalley group of type f4. In: St. Petersburg Mathematical Journal. 2010 ; Vol. 21, No. 5. pp. 819-823.

BibTeX

@article{f2193fa6fbb842f79f884c07fa6215b1,
title = "Identity with constants in a chevalley group of type f4",
abstract = "N. L. Gordeev proved that a generalized group identity holds in Chevalley groups with multiply laced root systems. It was also shown that a stronger identity is valid for the Chevalley groups of types Bl and Cl. In the present paper, it is proved that this strong identity is fulfilled in Chevalley groups of type F4 and fails to be true in Chevalley groups of type G2. The main result of the paper is the last ingredient in the proof of the claim that the lattice of intermediate subgroups between G(F4,R) and G(F4,A) is standard for an arbitrary pair of rings R ⊆ A with 2 invertible.",
keywords = "Chevalley group, Group identity, Multiply laced root system",
author = "V. Nesterov and A. Stepanov",
year = "2010",
month = dec,
day = "1",
doi = "10.1090/S1061-0022-2010-01119-1",
language = "English",
volume = "21",
pages = "819--823",
journal = "St. Petersburg Mathematical Journal",
issn = "1061-0022",
publisher = "American Mathematical Society",
number = "5",

}

RIS

TY - JOUR

T1 - Identity with constants in a chevalley group of type f4

AU - Nesterov, V.

AU - Stepanov, A.

PY - 2010/12/1

Y1 - 2010/12/1

N2 - N. L. Gordeev proved that a generalized group identity holds in Chevalley groups with multiply laced root systems. It was also shown that a stronger identity is valid for the Chevalley groups of types Bl and Cl. In the present paper, it is proved that this strong identity is fulfilled in Chevalley groups of type F4 and fails to be true in Chevalley groups of type G2. The main result of the paper is the last ingredient in the proof of the claim that the lattice of intermediate subgroups between G(F4,R) and G(F4,A) is standard for an arbitrary pair of rings R ⊆ A with 2 invertible.

AB - N. L. Gordeev proved that a generalized group identity holds in Chevalley groups with multiply laced root systems. It was also shown that a stronger identity is valid for the Chevalley groups of types Bl and Cl. In the present paper, it is proved that this strong identity is fulfilled in Chevalley groups of type F4 and fails to be true in Chevalley groups of type G2. The main result of the paper is the last ingredient in the proof of the claim that the lattice of intermediate subgroups between G(F4,R) and G(F4,A) is standard for an arbitrary pair of rings R ⊆ A with 2 invertible.

KW - Chevalley group

KW - Group identity

KW - Multiply laced root system

UR - http://www.scopus.com/inward/record.url?scp=84871405020&partnerID=8YFLogxK

U2 - 10.1090/S1061-0022-2010-01119-1

DO - 10.1090/S1061-0022-2010-01119-1

M3 - Article

AN - SCOPUS:84871405020

VL - 21

SP - 819

EP - 823

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 5

ER -

ID: 36691978