equivalence classes of extensions of a group

例句：

1. 1. In mathematics,equivalence classes are used to describesets of objects that are considered equal insome sense.
   在数学中，等价类用于描述在某种意义上被视为相等的对象集合。
2. 2.The equivalence classes werecreated by assigning different weights to theelements within each class.
   这些等价类是通过给每个类的元素分配不同的权重来创建的。
3. 3. The study of equivalence classes is important in understanding the structureand behavior of complex systems.
   研究等价类对于理解复杂系统的结构与行为至关重要。