Abstract Like the lower central series of a nilpotent group, filters generalize the connection between nilpotent groups and graded Lie rings. However, unlike the case with the lower central series, the associated graded Lie ring may share few features with the original group: e.g. the associated Lie ring can be trivial or arbitrarily large. We determine properties of filters such that every isomorphism between groups is induced by an isomorphism between graded Lie rings.

中文翻译：

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与同构测试兼容的过滤器

摘要 与幂零群的下中心级数一样，滤波器概括了幂零群和分级李环之间的联系。然而，与较低中心级数的情况不同，相关的分级李环可能与原始组共享很少的特征：例如，相关的李环可以是微不足道的或任意大的。我们确定滤波器的属性，使得组之间的每个同构都是由分级 Lie 环之间的同构引起的。