论文标题
Auslander猜想的尺寸少于7
The Auslander conjecture for dimension less then 7
论文作者
论文摘要
1964年，奥斯兰氏菌（L. Auslander）猜想，仿射基团的每个晶体学亚组几乎都是可以解决的，即包含一个有限指数的可解决的亚组。 D. Fried和W. Goldman使用共同体论证证明了Auslander对N = 3的猜想。我们证明了N <7的Auslander猜想。证明主要基于动态论点。在某些情况下，我们使用可以避免的共同体论点，但它会大大延长证据。
In 1964 L. Auslander conjectured that every crystallographic subgroup of an the affine group is virtually solvable, i.e. contains a solvable subgroup of finite index. D. Fried and W. Goldman proved Auslander's conjecture for n = 3 using cohomological arguments. We prove the Auslander conjecture for n < 7. The proof is based mainly on dynamical arguments. In some cases, we use the cohomological argument which we could avoid but it would significantly lengthen the proof.
