On the product decomposition conjecture for finite simple groups

Nick Gill; László Pyber; Ian Short; Endre Szabó

On the product decomposition conjecture for finite simple groups

Group Theory 2012-05-18 v2

Authors: Nick Gill , László Pyber , Ian Short , Endre Szabó

Abstract

We prove that if $G$ is a finite simple group of Lie type and $S$ a subset of $G$ of size at least two then $G$ is a product of at most $c\log|G|/\log|S|$ conjugates of $S$ , where $c$ depends only on the Lie rank of $G$ . This confirms a conjecture of Liebeck, Nikolov and Shalev in the case of families of simple groups of Lie type of bounded rank.

Keywords

finite group theory conjugacy classes in groups group theory

Cite

@article{arxiv.1111.3497,
  title  = {On the product decomposition conjecture for finite simple groups},
  author = {Nick Gill and László Pyber and Ian Short and Endre Szabó},
  journal= {arXiv preprint arXiv:1111.3497},
  year   = {2012}
}

Comments

13 pages. In this version a number of new results are added which generalize some classical results of additive combinatorics to the non-abelian setting

On the product decomposition conjecture for finite simple groups

Abstract

Keywords

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