A REFINED WARING PROBLEM FOR FINITE SIMPLE GROUPS

Michael Larsen, Pham Huu Tiep

Research output: Contribution to journalArticle

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

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

Fingerprint Dive into the research topics of 'A REFINED WARING PROBLEM FOR FINITE SIMPLE GROUPS'. Together they form a unique fingerprint.

  • Cite this