On the Modular Isomorphism Problem for groups of class 3 and obelisks
Leo Margolis and Mima Stanojkovski
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Submission date: 02. Oct. 2020
MSC-Numbers: 20C05, 20D15, 16U60
Keywords and phrases: Modular Isomorphism Problem, modular group algebra, finite p-groups, small group algebra
Link to arXiv: See the arXiv entry of this preprint.
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.