Higher commutativity and nilpotency in finite groups

Details Higher commutativity and nilpotency in finite groups Higher commutativity and nilpotency in finite groups

2010-05-21

arxiv.org/abs/1005.3876v1

Mathematics

Group Theory

16 pages. Preliminary version

Scientific paper

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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