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A generalization of the diameter bound of Liebeck and Shalev for finite simple groups
Acta Mathematica Hungarica ( IF 0.9 ) Pub Date : 2021-06-12 , DOI: 10.1007/s10474-021-01152-8
A. Maróti , L. Pyber

Let \(G\) be a non-abelian finite simple group. A famous result of Liebeck and Shalev is that there is an absolute constant \(c\) such that whenever \(S\) is a non-trivial normal subset in \(G\) then \(S^{k} = G\) for any integer \(k\) at least \(c \cdot (\log|G|/\log|S|)\). This result is generalized by showing that there exists an absolute constant \(c\) such that whenever \(S_{1}\), \(\ldots , \) \(S_{k}\) are normal subsets in \(G\) with \(\prod_{i=1}^{k} |S_{i}| \geq {|G|}^{c}\) then \(S_{1} \cdots S_{k} = G\).



中文翻译:

有限单群的 Liebeck 和 Shalev 直径界的推广

\(G\)是一个非阿贝尔有限单群。Liebeck 和 Shalev 的一个著名结果是存在一个绝对常数\(c\)使得只要 \(S\)\(G\) 中的一个非平凡正规子集,那么\(S^{k} = G \)对于任何整数\(k\)至少 \(c \cdot (\log|G|/\log|S|)\)。通过表明存在绝对常数\(c\)使得\(S_{1}\) , \(\ldots , \) \(S_{k}\)\( G\)\(\prod_{i=1}^{k} |S_{i}| \geq {|G|}^{c}\)然后\(S_{1} \cdots S_{k} = G\)

更新日期:2021-06-13
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