论文标题
单词图像及其冒名顶替者在有限的nilpotent群体中
Word Images and Their Impostors in Finite Nilpotent Groups
论文作者
论文摘要
Lubotzky在2014年表明，包含身份的有限简单组的自动形态不变子集总是单词图像。在本文中，我们研究了有限的nilpotent组的单词图，并表明，对于任意有限的组，包含不是单词图像的身份的自动形态不变子集的数量，称为单词图像冒名顶替者，可能会大于实际单词图像的数量。在此过程中，我们在nilpotent $ 2 $的nilpotent群体上构建了一套$ 2 $的避免单词地图，并在某些情况下证明了它的最低限度。
It was shown by Lubotzky in 2014 that automorphism invariant subsets of finite simple groups which contain identity are always word images. In this article, we study word maps on finite nilpotent groups and show that for arbitrary finite groups, the number of automorphism invariant subsets containing identity which are not word images, referred to as word image impostors, may be arbitrarily larger than the number of actual word images. In the course of it, we construct a $2$-exhaustive set of word maps on nilpotent groups of class $2$ and demonstrate its minimality in some cases.
