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

We study the Modular Isomorphism Problem for groups of small order based on an improvement algorithm described by Eick. Our allows to determine quotients I(kG)/I(kG)m augmentation ideal without first computing full I(kG). computations yield a positive answer MIP 37 and strongly reduce cases that need be checked 56. also show counterexamples found recently García-Lucas, Margolis del Río are only 2- or 3-generated 29. Furthermore, we provide proof observation Bagiński, which is helpful in eliminating computationally difficult cases.