JournalsggdVol. 7, No. 4pp. 867–882

On the product decomposition conjecture for finite simple groups

  • Nick Gill

    Open University, Milton Keynes, UK
  • László Pyber

    Hungarian Academy of Sciences, Budapest, Hungary
  • Ian Short

    Open University, Milton Keynes, UK
  • Endre Szabó

    Hungarian Academy of Sciences, Budapest, Hungary
On the product decomposition conjecture for  finite simple groups cover
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Abstract

We prove that if GG is a finite simple group of Lie type and SS is a subset of GG of size at least two, then GG is a product of at most clogG/logSc\log|G|/\log|S| conjugates of SS, where cc depends only on the Lie rank of GG. This confirms a conjecture of Liebeck, Nikolov and Shalev in the case of families of simple groups of bounded rank. We also obtain various related results about products of conjugates of a set within a group.

Cite this article

Nick Gill, László Pyber, Ian Short, Endre Szabó, On the product decomposition conjecture for finite simple groups. Groups Geom. Dyn. 7 (2013), no. 4, pp. 867–882

DOI 10.4171/GGD/208