A generalization of a theorem of Rodgers and Saxl for simple groups of bounded rank

Nick Gill, Laszlo Pyber, Endre Szabo

Research output: Contribution to journalArticlepeer-review

2 Downloads (Pure)

Abstract

We prove that if $G$ is a finite simple group of Lie type and $S_1,\dots, S_k$ are subsets of $G$ satisfying $\prod_{i=1}^k|S_i|\geq|G|^c$ for some $c$ depending only on the rank of $G$, then there exist elements $g_1,\dots, g_k$ such that $G=(S_1)^{g_1}\cdots (S_k)^{g_k}$. This theorem generalizes an earlier theorem of the authors and Short.

We also propose two conjectures that relate our result to one of Rodgers and Saxl pertaining to conjugacy classes in $\SL_n(q)$, as well as to the Product Decomposition Conjecture of Liebeck, Nikolov and Shalev.
Original languageEnglish
Pages (from-to)464-471
Number of pages8
JournalBulletin of the London Mathematical Society
Volume52
Issue number3
DOIs
Publication statusPublished - 21 May 2020

Keywords

  • 20D06
  • 20D40 (primary)
  • 20E45 (secondary)

Fingerprint

Dive into the research topics of 'A generalization of a theorem of Rodgers and Saxl for simple groups of bounded rank'. Together they form a unique fingerprint.

Cite this