标题： ${\rm SK}_1$类似正交群的可解性 显示英文标题

标题： Solvability of the ${\rm SK}_1$-analog of the orthogonal groups

摘要： 我们证明了相对Dickson-Siegel-Eichler-Roy(DSER)初等正交群的扩张原理，并利用扩张原理证明了该群的Quillen关于局部-整体原理的类似定理。 应用相对局部-整体原理，我们证明了正交群的${\rm SK_1}$类似物的可解性和幂零性，并研究了奇初等正交群的同伦和交换性原理。 显示英文摘要

摘要： We prove the dilation principle for the relative Dickson-Siegel-Eichler-Roy (DSER) elementary orthogonal group and using the dilation principle we prove the Quillen's analog of the local-global principle for the group. Applying the relative local-global principle, we prove the solvability and nilpotency of the ${\rm SK_1}$-analog of the orthogonal groups and study the homotopy and commutativity principle for odd elementary orthogonal groups.