有限群的高交换性与幂零性
Higher commutativity and nilpotency in finite groups
摘要：
考虑生成幂零子群的有限群中的有序元组。给定一个整数$q$，我们考虑类小于$q$的幂零子群的偏序集及其相应的陪集偏序集.这些偏序集产生了一族由幂零子群类参数化的有限狄利克雷级数，这反过来又反映了由这些子群确定的概率和拓扑不变量。讨论了这些级数与群的分类空间的滤子的关系。
英文摘要：
We consider ordered tuples in finite groups generating nilpotent subgroups. Given an integer $q$ we consider the poset of nilpotent subgroups of class less than $q$ and its corresponding coset poset. These posets give rise to a family of finite Dirichlet series parametrized by the nilpotency class of the subgroups, which in turn reflect probabilistic and topological invariants determined by these subgroups. Connections of these series to filtrations of classifying spaces of a group are discussed.
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