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On the modular isomorphism problem for groups of class 3 and obelisks

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Abstract 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… Click to show full abstract

Abstract 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 ????-group from the structure of the associated modular group algebra. Finally, we study the class of so-called ????-obelisks which are highlighted by recent computer-aided investigations of the problem.

Keywords: isomorphism problem; class; group; modular isomorphism; problem

Journal Title: Journal of Group Theory
Year Published: 2021

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