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arXiv · 2603.09363

The group identification problem for $p$-groups of small order

Bettina Eick·Henrik Schanze
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Abstract

We investigate which group-theoretic invariants are powerful in distinguishing among non-isomorphic p-groups. Based on this, we devise an effective algorithm to solve the group identification problem for the $10,494,213$ groups of order $2^9$. We exhibit 56 pairs of groups of order $2^9$ which are difficult to distinguish by invariants.

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Bettina Eick, Henrik Schanze. 2026-03-10. The group identification problem for $p$-groups of small order. https://doi.org/10.46298/jgcc.2026.18.2.17698

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