{"paper":{"title":"Kirillov's orbit method and polynomiality of the faithful dimension of $p$-groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.NT"],"primary_cat":"math.RT","authors_text":"Hadi Salmasian, Keivan Mallahi-Karai, Mohammad Bardestani","submitted_at":"2017-12-06T03:17:33Z","abstract_excerpt":"Given a finite group $\\mathrm{G}$ and a field $K$, the faithful dimension of $\\mathrm{G}$ over $K$ is defined to be the smallest integer $n$ such that $\\mathrm{G}$ embeds into $\\mathrm{GL}_n(K)$. In this paper we address the problem of determining the faithful dimension of a $p$-group of the form $\\mathscr{G}_q:=\\exp(\\mathfrak{g} \\otimes_\\mathbb{Z}\\mathbb{F}_q)$ associated to $\\mathfrak{g}_q:=\\mathfrak{g} \\otimes_\\mathbb{Z}\\mathbb{F}_q$ in the Lazard correspondence, where $\\mathfrak{g}$ is a nilpotent $\\mathbb{Z}$-Lie algebra which is finitely generated as an abelian group. We show that in gen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02019","kind":"arxiv","version":3},"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"}