{"paper":{"title":"Extension of elementary $p$-groups and its application in classification of groups of prime exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Chi Zhang, Yu Ye, Zheyan Wan","submitted_at":"2020-03-28T14:52:10Z","abstract_excerpt":"Let $p$ be a prime number and $\\mathbb{Z}_p=\\mathbb{Z}/p\\mathbb{Z}$. We study finite groups with abelian derived subgroup and exponent $p$ in terms of group extension data and their matrix presentations. We show a one-to-one correspondence between the following two sets: (i) the isoclasses of class 2 groups of exponent $p$ and order $p^{m+n}$ and with derived subgroup $\\mathbb{Z}_p^n$, and (ii) the set $\\text{Gr}(n,\\text{AS}_m(\\mathbb{Z}_p))/\\text{GL}_m(\\mathbb{Z}_p)$ of orbits of $\\text{Gr}(n,\\text{AS}_m(\\mathbb{Z}_p))$ under the congruence action by $\\text{GL}_m(\\mathbb{Z}_p)$, where $\\text{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.12802","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2003.12802/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}