{"paper":{"title":"Some restrictions on normalizers or centralizers in finite p-groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Antonio Tortora, Gustavo A. Fernandez-Alcober, Leire Legarreta, Maria Tota","submitted_at":"2013-11-11T21:16:32Z","abstract_excerpt":"We study three restrictions on normalizers or centralizers in finite p-groups, namely: (i) |N_G(H) : H| <= p^k for every H non-normal in G, (ii) |N_G(<g>) : <g>| <= p^k for every <g> non-normal in G, and (iii) |C_G(g) : <g>| <= p^k for every <g> non-normal in G. We prove that (i) and (ii) are equivalent, and that the order of a non-Dedekind finite p-group satisfying any of these three conditions is bounded for p>2. More precisely, we get the best possible bound for the order of G in all three cases, which is |G| <= p^{2k+2}. The order of the group cannot be bounded for p=2, but we are able to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2608","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"}