{"paper":{"title":"Semi-extraspecial groups with an abelian subgroup of maximal possible order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mark L. Lewis","submitted_at":"2017-10-27T18:48:29Z","abstract_excerpt":"Let $p$ be a prime. A $p$-group $G$ is defined to be semi-extraspecial if for every maximal subgroup $N$ in $Z(G)$ the quotient $G/N$ is a an extraspecial group. In addition, we say that $G$ is ultraspecial if $G$ is semi-extraspecial and $|G:G'| = |G'|^2$. In this paper, we prove that every $p$-group of nilpotence class $2$ is isomorphic to a subgroup of some ultraspecial group. Given a prime $p$ and a positive integer $n$, we provide a framework to construct of all the ultraspecial groups order $p^{3n}$ that contain an abelian subgroup of order $p^{2n}$. In the literature, it has been proved"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10299","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":""},"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"}