A REFINED WARING PROBLEM FOR FINITE SIMPLE GROUPS

Michael Larsen, Pham Huu Tiep

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let w1 and w2 be nontrivial words in free groups Fn1 and Fn2, respectively. We prove that, for all sufficiently large finite nonabelian simple groups G, there exist subsets C1 ⊆ w1(G) and C2 ⊆ w2(G) such that |Ci| = O(|G|1/2 log1/2 |G|) and C1C2 = G. In particular, if w is any nontrivial word and G is a sufficiently large finite nonabelian simple group, then w(G) contains a thin base of order 2. This is a nonabelian analog of a result of Van Vu ['On a refinement of Waring's problem', Duke Math. J. 105(1) (2000), 107-134.] for the classical Waring problem. Further results concerning thin bases of G of order 2 are established for any finite group and for any compact Lie group G.

Original languageEnglish (US)
Article numbere6
JournalForum of Mathematics, Sigma
Volume3
DOIs
StatePublished - Jan 1 2015

ASJC Scopus subject areas

  • Analysis
  • Theoretical Computer Science
  • Algebra and Number Theory
  • Statistics and Probability
  • Mathematical Physics
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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