论文标题
与对称组的常数单词地图
Word maps with constants on symmetric groups
论文作者
论文摘要
我们在对称组上使用常数研究单词图。即使对所有对称组有效的有界长度的身份混合身份，我们也表明，这种身份在公制意义上没有。此外，我们证明，用常数和非平凡内容的单词映射仅根据单词的长度，具有正直径的图像。最后，我们还表明，在有限的非亚洲简单组上，每个自动图$ g \ g \ g $实际上是一个单词映射，带有$ g $的常数。
We study word maps with constants on symmetric groups. Even though there are mixed identities of bounded length that are valid for all symmetric groups, we show that no such identities hold in a metric sense. Moreover, we prove that word maps with constants and non-trivial content that are short enough have an image of positive diameter only depending on the length of the word. Finally, we also show that every self-map $G \to G$ on a finite non-abelian simple group is actually a word map with constants from $G$.
