论文标题
在$ \ mathrm {psl} _ {2}（\ mathbb {f} _ {q}）$上的非解释单词地图上
On non-surjective word maps on $\mathrm{PSL}_{2}(\mathbb{F}_{q})$
论文作者
论文摘要
jambor-liebeck-o'brien表明，存在非proper-power单词映射，这些单词映射在$ \ mathrm {psl} _ {2}（\ Mathbb {f} _ {q} _ {q}）$上没有汇总，对于无限的许多$ q $。这为Shalev的猜想提供了第一个反例，该示例指出，如果两个可变性的单词不是非客气单词的适当力量，那么相应的单词映射是在$ \ mathrm {psl} _2 _2（\ mathbb {f} _ {q} _ {q}）上的$ \ mathrm {psl} _2 _ {q} _ {q}）$。在他们的工作中，我们构建了这些类型的非解放单词地图的新示例。作为一个应用程序，我们在$ \ Mathbb Q $的绝对Galois组上获得了非解释的单词地图。
Jambor--Liebeck--O'Brien showed that there exist non-proper-power word maps which are not surjective on $\mathrm{PSL}_{2}(\mathbb{F}_{q})$ for infinitely many $q$. This provided the first counterexamples to a conjecture of Shalev which stated that if a two-variable word is not a proper power of a non-trivial word, then the corresponding word map is surjective on $\mathrm{PSL}_2(\mathbb{F}_{q})$ for all sufficiently large $q$. Motivated by their work, we construct new examples of these types of non-surjective word maps. As an application, we obtain non-surjective word maps on the absolute Galois group of $\mathbb Q$.
