{"paper":{"title":"The M\\\"obius function of ${\\rm PSU}(3,2^{2^n})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Giovanni Zini","submitted_at":"2018-07-24T13:19:14Z","abstract_excerpt":"Let $G$ be the simple group ${\\rm PSU}(2,2^{2^n})$, $n>0$. For any subgroup $H$ of $G$, we compute the M\\\"obius function $\\mu_L(H,G)$ of $H$ in the subgroup lattice $L$ of $G$, and the M\\\"obius function $\\mu_{\\bar L}([H],[G])$ of $[H]$ in the poset $\\bar L$ of conjugacy classes of subgroups of $G$. For any prime $p$, we provide the Euler characteristic of the order complex of the poset of $p$-subgroups of $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09086","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"}