Investigation reveals challenges in identifying non-isomorphic p-groups of order 2^9, suggesting improvements in algorithms for group identification.
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 2⁹. We exhibit 56 pairs of groups of order 2⁹ which are difficult to distinguish by invariants. 13 pages
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Eick et al. (2026) studied this question.
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