组合Hantzsche-Wendt群的性质
Properties of the combinatorial Hantzsche-Wendt groups
摘要：
组合Hantzsche-Wendt群G（n）由W.克雷格和P.A.林内尔当n = 2时，它是三维定向平坦流形的一个基本群，不含循环和乐群。我们计算了G（n），n > 0的具有Q和F2系数的Hilbert-Poincare级数.证明了G（n）的上同调维数等于n + 1.还考虑了这个群的一些其他性质。
英文摘要：
Combinatorial Hantzsche-Wendt groups G(n) were defined by W. Craig and P. A. Linnell. For n = 2 it is a fundamental group of 3-dimensional oriented flat manifold with no cyclic holonomy group. We calculate the Hilbert-Poincare series of G(n), n > 0 with Q and F2 coefficients. Moreover, we prove that a cohomological dimension of G(n) is equal to n + 1. Some other properties of this group are also considered.
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