发表机构
Dundalk Institute of Technology（邓莱克理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究解决了模群代数下与上李幂零指数问题的剩余情形，在特征2和3下证明两指数相等，完成有限域上素数幂阶有限群的相关问题，引入终端限制PBW构造完成论证。
AI 中文摘要
我们解决了关于模群代数的下与上李幂零指数这一长期存在问题的剩余情形。自1992年以来，人们已知特征大于3时这两个指数相等；我们在剩余的特征2和特征3情形下证明了该等式，从而完成了有限域上素数幂阶有限群的相关问题。该证明对每个素数给出了统一论证，并引入了一种终端限制庞加莱-伯克霍夫-维特（Poincaré-Birkhoff-Witt）构造，将下李问题转化为时序可达性论证，且对导出子群无结构假设。
英文摘要
We resolve the remaining cases of a longstanding problem on the lower and upper Lie nilpotency indices of modular group algebras. Equality of the two indices has been known in characteristics greater than three since 1992; we establish it in the remaining characteristics two and three, thereby completing the problem for finite groups of prime-power order over finite fields. The proof gives a uniform argument for every prime and introduces a terminal restricted Poincare-Birkhoff-Witt construction that converts the lower-Lie problem into a chronological reachability argument, with no structural hypothesis on the derived subgroup.
Comments39 pages
