关于半直积Z^n r乘Z/m的群上同调及Adem-Ge-Pan-Petrosyan的一个猜想
On the group cohomology of the semi-direct product Z^n rtimes Z/m and a conjecture of Adem-Ge-Pan-Petrosyan
摘要：
考虑半直积Z^n r乘以Z/m。Adem-Ge-Pan-Petrosyan的一个猜想预言了相关的Lyndon-Hochschild-Serre谱序列的坍缩。我们证明了这个猜想，条件是Z^n上的Z/m-作用在原点外是自由的。我们在一般情况下证明了这个猜想是错误的，即我们给出了一个例子，其中n=6，m=4，二阶微分不为零。
英文摘要：
Consider the semi-direct product Z^n rtimes Z/m. A conjecture of Adem-Ge-Pan-Petrosyan predicts that the associated Lyndon-Hochschild-Serre spectral sequence collapses. We prove this conjecture provided that the Z/m-action on Z^n is free outside the origin. We disprove the conjecture in general, namely, we give an example with n=6 and m=4, where the second differential does not vanish.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
