For a non-elementary discrete isometry group $G$ of divergence type acting on a proper geodesic $delta$-hyperbolic space, we prove that its Patterson measure is quasi-invariant under the normalizer of $G$. As applications of this result, we have: (1) under a minor assumption, such a discrete group $G$ admits no proper conjugation, that is, if the conjugate of $G$ is contained in $G$, then it coincides with $G$; (2) the critical exponent of any non-elementary normal subgroup of $G$ is strictly greater than the half of that for $G$.

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Gromov双曲空间离散组的归一化，散度类型和Patterson度量

对于作用在适当测地线δ双曲空间上的发散类型的非基本离散等轴测图组$ G $，我们证明了在$ G $的归一化条件下，其Patterson测度是准不变的。作为该结果的应用，我们有：（1）在一个较小的假设下，这样的离散组$ G $不接受适当的共轭，即，如果$ G $的共轭包含在$ G $中，则它与$ G $; （2）$ G $的任何非基本正常子组的临界指数严格大于$ G $的临界指数的一半。