If moreover the automorphism involved is of finite order, some special orbits are related to the nonabelian cohomology of a finite cyclic group. 当扭共轭作用中的自同构为有限阶时,某些特殊的轨道对应于有限循环群的非交换上同调。
But twisted conjugate actions of Lie groups have closed relation with nonabelian cohomology of cyclic groups with coefficients in Lie groups. 而李群的扭共轭作用与循环群以李群为系数的非交换上同调有非常密切的关系。