发表机构
Oregon State University（俄勒冈州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文肯定回答了Knill提出的问题，证明每个反射群都存在至多七值的右不变度量，使其全等距群恰为右正则作用，从而每个反射群都是自然的。
AI 中文摘要
我们所说的反射群，是指由非恒等对合生成的抽象群。Knill 证明了，基数至多为连续统的每个反射群都是自然的，即存在某个度量，使得在该度量下，其群结构在所有右平移为等距的群结构中同构意义下被确定；他并询问基数假设能否被去掉。我们肯定地回答了这个问题。更精确地说，每个反射群 G 都容许一个右不变度量，该度量至多取七个值，且其全等距群恰为 G 的右正则作用。证明用对良序无冗余生成集上刚性图的有限值编码，取代了生成元上不同的数值标签。
英文摘要
By a reflection group we mean an abstract group generated by nonidentity involutions. Knill proved that every reflection group of cardinality at most the continuum is natural, in the sense that some metric determines its group structure up to isomorphism among group structures whose right translations are isometries, and asked whether the cardinality hypothesis can be removed. We answer this question affirmatively. More precisely, every reflection group G admits a right invariant metric taking at most seven values for which the full isometry group is the right-regular action of G. The proof replaces distinct numerical labels on generators by a finite-valued encoding of a rigid graph on a well-ordered irredundant generating set.
Comments7 pages
