We prove some new relations between weak approximation and some rationalequivalence relations (Brauer and R-equivalence) in algebraic groups overarithmetical fields. By using weak approximation and local - global approach,we compute completely the group of Brauer equivalence classes of connectedlinear algebraic groups over number fields, and also completely compute thegroup of R-equivalence classes of connected linear algebraic groups $G$, whicheither are defined over a totally imaginary number field, or contains noanisotropic almost simple factors of exceptional type $^{3,6}D_4$, nor $E_6$.We discuss some consequences derived from these, e.g., by giving some newcriteria for weak approximation in algebraic groups over number fields, byindicating a new way to give examples of non stably rational algebraic groupsover local fields and application to norm principle.
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机译：我们证明了算术场中代数群中弱逼近与一些合理等价关系（Brauer和R-等价关系）之间的一些新关系。通过使用弱逼近和局部-全局方法，我们可以完全计算数字场上连通线性代数组的Brauer等价类组，还可以完全计算连通线性代数组$ G $的R-等价类组一个完全虚数的字段，或者包含异常类型$ ^ {3,6} D_4 $或$ E_6 $的各向异性的几乎简单的因子。我们讨论了由此产生的一些结果，例如，通过给出一些弱近似的新准则数域上的代数群，指出了一种新的方法，给出了局部域上非稳定有理代数群的例子，并适用于范数原理。
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