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

Nick Gill, Laszlo Pyber, Endre Szabo

    Allbwn ymchwil: Cyfraniad at gyfnodolynErthygladolygiad gan gymheiriaid

    2 Wedi eu Llwytho i Lawr (Pure)

    Crynodeb

    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.
    Iaith wreiddiolSaesneg
    Tudalennau (o-i)464-471
    Nifer y tudalennau8
    CyfnodolynBulletin of the London Mathematical Society
    Cyfrol52
    Rhif cyhoeddi3
    Dynodwyr Gwrthrych Digidol (DOIs)
    StatwsCyhoeddwyd - 21 Mai 2020

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