http://orcid.org/0000-0002-6913-1979
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Abstract
The modular isomorphism problem is settled for 3-groups of maximal class but two families of groups. Moreover, the conjecture that the ideals belonging to the lower central series of a group base are determined by the structure of the group algebra is refuted in greatest generality by virtue of a single group of order 81 of maximal class, and it is proved that the nilpotency class is determined by the structure of the group algebra for p-groups of maximal class.
2010 MATHEMATICS SUBJECT CLASSIFICATION:
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No potential conflict of interest was reported by the authors.
Additional information
Funding
The research of the first author was supported by the Bialystok University of Technology grant S/WI/1/2014 and funded by resources for research by the Ministry of Science and Higher Education of Poland. These resources also funded the stay of the second author at Bialystok University, who was also supported by University of Nyíregyháza grant No. IHK/200-13/2017.