Product decompositions in finite simple groups

Martin W. Liebeck*, Nikolay Nikolov, Aner Shalev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrary finite simple groups, and for large subsets of groups of Lie type of bounded rank. Some of our arguments apply recent advances in the theory of growth in finite simple groups of Lie type, and provide a variety of new product decompositions of these groups.

Original languageAmerican English
Pages (from-to)469-472
Number of pages4
JournalBulletin of the London Mathematical Society
Issue number3
StatePublished - Jun 2012

Bibliographical note

Funding Information:
The authors are grateful for the support of an Engineering and Physical Sciences Research Council grant. The third author is also grateful for the support of an European Research Council Advanced Grant 247034.


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