AI 中文总结
本文通过构造根对合并引入点对合与线对合，给出了厚极空间Moufang性质的等价定义，证明了所有有限及无限秩厚极空间均为Moufang。
AI 中文摘要
我们提供了嵌入在更高有限秩的厚极空间中的厚广义四边形的非平凡根对合的直接构造，并证明了所有这些根对合都可以表示为长度为$4$的自投影。这明确揭示了有限秩厚极空间的小射影群与特殊射影群之间的联系。我们还证明了所构造的根对合可以扩展到环境极空间。此外，我们引入了点对合和线对合，并利用它们在不使用公寓概念的情况下给出了厚极空间Moufang性质的等价定义。这反过来又使我们能够定义无限秩厚极空间的Moufang性质。因此，我们证明了所有有限秩和无限秩的厚极空间都是Moufang的。
英文摘要
We provide direct constructions of nontrivial root elations of thick generalized quadrangles embedded in thick polar spaces of higher finite rank and show that all of these can be expressed as self-projectivities of length $4$. This reveals a connection between the little projective groups and the special projectivity groups of thick polar spaces of finite rank explicitly. We also prove that the constructed root elations extend to the ambient polar space. Furthermore, we introduce point elations and line elations and use them to give an equivalent definition of the Moufang property for thick polar spaces, without using the notion of apartments. This, in turn, allows us to define the Moufang property for thick polar spaces of infinite rank. Consequently, we show that all thick polar spaces of finite and infinite rank are Moufang.
Journal refJournal of Geometry, vol. 117, article no. 37 (2026)
DOI：10.1007/s00022-026-00820-w
