论文标题
关于3级和方尖碑组的模块化同构问题
On the Modular Isomorphism Problem for groups of class 3 and obelisks
论文作者
论文摘要
我们研究了现有技术和新技术的组合，研究模块化同构问题。我们利用小组代数为两类nilpotency 3类提供了积极的答案。我们还引入了一种新方法，以从相关模块化组代数的结构中得出有限的$ p $ group的下中央系列的属性。最后，我们研究了所谓的$ p $ obelisks的类别，这些类别是最近对该问题的计算机辅助调查所强调的。
We study the Modular Isomorphism Problem applying a combination of existing and new techniques. We make use of the small group algebra to give a positive answer for two classes of groups of nilpotency class 3. We also introduce a new approach to derive properties of the lower central series of a finite $p$-group from the structure of the associated modular group algebra. Finally, we study the class of so-called $p$-obelisks which are highlighted by recent computer-aided investigations of the problem.
