In this note we obtain estimates on the relative growth of normal subgroups of non-elementary hyperbolic groups, particularly those with free abelian quotient. As a corollary, we deduce that the associated relative growth series fail to be rational.

中文翻译：

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双曲族的相对增长

在本说明中，我们获得了对非基本双曲组的正常子组（尤其是具有自由阿贝尔商数的子组）的相对增长的估计。作为推论，我们推断相关的相对增长序列不合理。