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

Mathematics > Group Theory [Submitted on 10 Mar 2026 (v1), last revised 16 Jun 2026 (this version, v2)] Title:The group identification problem for $p$-groups of small order View PDF HTML (experimental)Abstract:We investigate which invariants of groups are powerful in distinguishing 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 a list of groups of order $2^9$ which are difficult to distinguish y invariants and thus are the most difficult cases for our algorithm. Submission history From: Bettina Eick [view email][v1] Tue, 10 Mar 2026 08:44:13 UTC (13 KB) [v2] Tue, 16 Jun 2026 15:11:49 UTC (14 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.