On the modular isomorphism problem for groups of class 3 and obelisks-Reference-Cited by-同舟云学术

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

Published:2021-09-14 Issue:1 Volume:25 Page:163-206
ISSN:1433-5883
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Margolis Leo¹,Stanojkovski Mima²

Affiliation:

1. Department of Mathematics , Vrije Universiteit Brussel , Pleinlaan 2, 1050 Brussels , Belgium

2. Max-Planck-Institut für Mathematik in den Naturwissenschaften , Inselstraße 22, 04103 Leipzig , Germany

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 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.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/jgth-2020-0174/pdf

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