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

^*Corresponding author for this work

Einstein Institute of Mathematics

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

15 Scopus citations

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

Bibliographical 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.

Keywords

Expander graphs
Finite simple groups
Subgroup width

Access to Document

10.1016/j.jalgebra.2008.12.030

Cite this

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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.",

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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.

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KW - Subgroup width

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