{"paper":{"title":"Overgroups of exterior powers of an elementary group. I. Levels and normalizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Ilia Nekrasov, Roman Lubkov","submitted_at":"2018-01-24T10:58:48Z","abstract_excerpt":"In the present paper, we prove the first part in the standard description of groups $H$ lying between $m$-th exterior power of elementary group $E(n,R)$ and the general linear group $GL_{\\binom{n}{m}}(R)$. We study structure of the exterior power of elementary group and its relative analog $E\\left(\\binom{n}{m},R,A\\right)$. In the considering case $n \\geq 3m$, the description is explained by the classical notion of level: for every such $H$ we find unique ideal $A$ of the ring $R$. Motivated by the problem, we prove the coincidence of the following groups: normalizer of the exterior power of el"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07918","kind":"arxiv","version":2},"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"}