{"paper":{"title":"Boosting an analogue of Jordan's theorem for finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexandre Turull, Ignasi Mundet i Riera","submitted_at":"2013-10-24T08:06:17Z","abstract_excerpt":"Let $\\mathcal C$ be a set of finite groups which is closed under taking subgroups and let $d$ and $M$ be positive integers. Suppose that for any $G\\in\\mathcal C$ whose order is divisible by at most two distinct primes there exists an abelian subgroup $A\\subseteq G$ such that $A$ is generated by at most $d$ elements and $[G : A] \\le M$. We prove that there exists a positive constant $C_0$ such that any $G \\in \\mathcal C$ has an abelian subgroup $A$ satisfying $[G : A] \\le C_0$, and $A$ can be generated by at most $d$ elements. We also prove some related results. Our proofs use the Classificatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6518","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"}