{"paper":{"title":"Commensurability growths of algebraic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Daniel Studenmund, Khalid Bou-Rabee, Tasho Kaletha","submitted_at":"2018-09-27T03:34:59Z","abstract_excerpt":"Fixing a subgroup $\\Gamma$ in a group $G$, the full commensurability growth function assigns to each $n$ the cardinality of the set of subgroups $\\Delta$ of $G$ with $[\\Gamma: \\Gamma \\cap \\Delta][\\Delta : \\Gamma \\cap \\Delta] \\leq n$. For pairs $\\Gamma \\leq G$, where $G$ is a Chevalley group scheme defined over $\\mathbb{Z}$ and $\\Gamma$ is an arithmetic lattice in $G$, we give precise estimates for the full commensurability growth, relating it to subgroup growth and a computable invariant that depends only on $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10332","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"}