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Group Numbers Reproducibility Project

In January 2016, I’ve asked on the Mathematics Q&A site the question called “Most wanted reproducible results in computational algebra“. I hope that making a list of suggested experiments to reproduce will be useful to those interested in checking them twice ;-). For example, one could submit their findings to a journal like ReScience which “targets computational research and encourages the explicit replication of already published research, promoting new and open-source implementations in order to ensure that the original research is reproducible”. If you have any suggestions, please consider posting them as answers to that question. Today I’ve also added my own answer, which I am reproducing below.

I believe that enumeration of finite groups of a given order is definitely among most wanted reproducible experiments. Here “enumeration” means providing complete and non-redundant list of groups, “complete” means that no groups are missing in this list, and “non-redundant” means that groups from this list are non-isomorphic pairwise. Guaranteeing these properties is crucial for results that rely on checking all groups of a given order, or that refer to a particular group by its “catalogue number”. (more…)