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

Summary · qwen2.5:32b

Research identifies effective group-theoretic invariants and develops an algorithm to distinguish among non-isomorphic p-groups, specifically applied to the $10,494,213$ groups of order $2^9$. Notably, 56 pairs of these groups are particularly challenging to differentiate using invariants.

Excerpt

arXiv:2603.09363v4 Announce Type: replace 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.