AI 中文总结
该研究证明有限群整同调的指数仅由次数和群指数界定，结合限制Burnside问题等方法，还运用Lyndon–Hochschild–Serre谱序列得到有限可解群等的明确界。
AI 中文摘要
我们证明，在每个固定次数下，有限群的整同调的指数仅由次数和该群的指数界定。该证明结合了限制Burnside问题的解决、棒构造的可表示性性质，可视为无环模型方法的扭 analogue（此处保留原词）。我们还运用Lyndon–Hochschild–Serre谱序列，针对有限可解群和幂零群，根据它们的导出长度和幂零类得到明确的界。
英文摘要
We prove that, in each fixed degree, the exponent of the integral homology of a finite group is bounded solely in terms of the degree and the exponent of the group. The proof combines the solution of the restricted Burnside problem with a representability property of the bar construction and may be viewed as a torsion analogue of the method of acyclic models. We also use the Lyndon--Hochschild--Serre spectral sequence to obtain explicit bounds for finite solvable and nilpotent groups in terms of their derived length and nilpotency class.
Comments8 pages
