Groups of Lie type as products of SL2 subgroups

Martin W. Liebeck*, Nikolay Nikolov, Aner Shalev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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 languageAmerican English
Pages (from-to)201-207
Number of pages7
JournalJournal of Algebra
Issue number1
StatePublished - 15 Jan 2011

Bibliographical note

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


  • Expander graphs
  • Finite simple groups
  • Subgroup width


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