The Modular Isomorphism Problem for small groups -- revisiting Eick's algorithm

2020/10/14 by Leo Margolis, Margolis, L., Tobias Moede +1 · 2 citations
Computer Science · Engineering · Mathematics · #16L60 #20C05 #20C40 #20D15 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings and Algebras (math.RA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2010.07030

openalex publication_date 2020/10/14 · openalex created_date 2020/10/22 · openalex updated_date 2026/07/28

Abstract

We study the Modular Isomorphism Problem (MIP) for groups of small order based on an improvement of an algorithm described by B. Eick. Our improvement allows to determine quotients I(kG)/I(kG)^m of the augmentation ideal without first computing the full augmentation ideal I(kG). It allows us to verify that the MIP has a positive answer for groups of order 3⁷ and to significantly reduce the cases that need to be checked for groups of order 5⁶. We further provide a proof for an observation of Bagiński and provide a negative answer to a question of Bleher, Kimmerle, Roggenkamp and Wursthorn.

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