标题： 单词映射在单群中的小像 显示英文标题

标题： Word maps with small image in simple groups

摘要： 我们构造非幂词，这些词在 SL(2; 22n) 中具有小像。特别是，相应的词映射不是满射的。我们还利用这一点构造词映射，其值恰好是单位元和一个17阶元素的等价类。在第二部分中，我们构造词，这些词的像由单位元和 Alt(n) 中一个等价类的元素组成，对于任何支持大小最多为10的等价类，适用于所有 n。 显示英文摘要

摘要： We construct non-power words which have small image in SL(2; 22n) for each n. In particular, the corresponding word maps are non-surjective. We also use this to construct word maps whose values are precisely the identity and a single equivalence class of elements of order 17. In the second part we construct words which have image consisting of the identity and a single equivalence class of elements in Alt(n) for all n for any equivalence class with support size at most 10.