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Remark by the authors regarding the preprint "The modular isomorphism problem": We have now come to realise that what we actually prove is not the complete solution to the problem, but rather the following: "By starting with an $\F_p$-algebra $A$, we can calculate all finite $p$-groups $G$ such that $A=\F_pG$." This explicit way of calculating these groups also gives a clear indication towards finding a counterexample, if such should exist, and solves the problem for many classes of groups. We wish to point out that everything in the paper is correct, except that the sequence $E$ in section 4 is not uniquely determined. This is what makes the problem still to be solved completely, and we would like to appologise for having overlooked this for so long, and to thank you for all your comments and questions. Another preprint will appear soon. Best wishes, Christin and Arnfinn