{"paper":{"title":"On Boolean intervals of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.OA","math.QA","math.RT"],"primary_cat":"math.GR","authors_text":"Mamta Balodi, Sebastien Palcoux","submitted_at":"2016-04-22T18:11:37Z","abstract_excerpt":"We prove a dual version of {\\O}ystein Ore's theorem on distributive intervals in the subgroup lattice of finite groups, having a nonzero dual Euler totient $\\hat{\\varphi}$. For any Boolean group-complemented interval, we observe that $\\hat{\\varphi} = \\varphi \\neq 0$ by the original Ore's theorem. We also discuss some applications in representation theory. We conjecture that $\\hat{\\varphi}$ is always nonzero for Boolean intervals. In order to investigate it, we prove that for any Boolean group-complemented interval $[H,G]$, the graded coset poset $\\hat{P} = \\hat{C}(H,G)$ is Cohen-Macaulay and t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06765","kind":"arxiv","version":7},"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"}