Groups of Lie type as products of SL2 subgroups

Martin W. Liebeck; Nikolay Nikolov; Aner Shalev

doi:10.1016/j.jalgebra.2008.12.030

Groups of Lie type as products of SL₂ subgroups

Martin W. Liebeck, Nikolay Nikolov, Aner Shalev

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

We prove that apart from the Suzuki groups, every finite simple group of Lie type of rank r over a field of q elements can be written as a product of C(r) subgroups isomorphic to SL₂(q) or PSL₂(q), where C(r) is a quadratic function. This has an application to the theory of expander graphs.

Original language	English
Pages (from-to)	201-207
Number of pages	7
Journal	Journal of Algebra
Volume	326
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2008.12.030
State	Published - 15 Jan 2011

Keywords

Expander graphs
Finite simple groups
Subgroup width

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Access to Document

10.1016/j.jalgebra.2008.12.030

Cite this

@article{25550cef911949988db102b10faa2a3b,

title = "Groups of Lie type as products of SL2 subgroups",

abstract = "We prove that apart from the Suzuki groups, every finite simple group of Lie type of rank r over a field of q elements can be written as a product of C(r) subgroups isomorphic to SL2(q) or PSL2(q), where C(r) is a quadratic function. This has an application to the theory of expander graphs.",

keywords = "Expander graphs, Finite simple groups, Subgroup width",

author = "Liebeck, {Martin W.} and Nikolay Nikolov and Aner Shalev",

note = "Funding Information: E-mail addresses: [email protected] (M.W. Liebeck), [email protected] (N. Nikolov), [email protected] (A. Shalev). 1 The author acknowledges the support of an EPSRC Visiting Fellowship at Imperial College London.",

year = "2011",

month = jan,

day = "15",

doi = "10.1016/j.jalgebra.2008.12.030",

language = "الإنجليزيّة",

volume = "326",

pages = "201--207",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Groups of Lie type as products of SL2 subgroups

AU - Liebeck, Martin W.

AU - Nikolov, Nikolay

AU - Shalev, Aner

N1 - Funding Information: E-mail addresses: [email protected] (M.W. Liebeck), [email protected] (N. Nikolov), [email protected] (A. Shalev). 1 The author acknowledges the support of an EPSRC Visiting Fellowship at Imperial College London.

PY - 2011/1/15

Y1 - 2011/1/15

N2 - We prove that apart from the Suzuki groups, every finite simple group of Lie type of rank r over a field of q elements can be written as a product of C(r) subgroups isomorphic to SL2(q) or PSL2(q), where C(r) is a quadratic function. This has an application to the theory of expander graphs.

AB - We prove that apart from the Suzuki groups, every finite simple group of Lie type of rank r over a field of q elements can be written as a product of C(r) subgroups isomorphic to SL2(q) or PSL2(q), where C(r) is a quadratic function. This has an application to the theory of expander graphs.

KW - Expander graphs

KW - Finite simple groups

KW - Subgroup width

UR - http://www.scopus.com/inward/record.url?scp=78649459885&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2008.12.030

DO - 10.1016/j.jalgebra.2008.12.030

M3 - مقالة

SN - 0021-8693

VL - 326

SP - 201

EP - 207

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -