Images of word maps in finite simple groups

Alexander Lubotzky

Images of word maps in finite simple groups

Group Theory 2012-11-29 v1

Authors: Alexander Lubotzky

Abstract

In response to questions by Kassabov, Nikolov and Shalev, we show that a given subset $A$ of a finite simple group $G$ is the image of some word map $w : G\times G\to G$ if and only if (i) $A$ contains the identity and (ii) $A$ is invariant under $\Aut (G)$ .

Keywords

word maps finite simple groups image identity element automorphism group group theory

Cite

@article{arxiv.1211.6575,
  title  = {Images of word maps in finite simple groups},
  author = {Alexander Lubotzky},
  journal= {arXiv preprint arXiv:1211.6575},
  year   = {2012}
}

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