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We prove the existence of a constant $C$, depending on $X$ but not on $\\omega$, such that any finite subgroup $G\\subset Ham(X,\\omega)$ has an abelian subgroup $A\\subseteq G$ satisfying $[G:A]\\leq C$, and $A$ can be generated by $n$ elements or fewer. If $b_1(X)=0$ we prove an analogous statement for the entire group of symplectomorphisms of $(X,\\omega)$. If $b_1(X)\\neq 0$ we prove the existence of a constant $C'$ depending only on $X$ such that any finite sub"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1605.05494","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-05-18T09:33:49Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"e1a18eb243a1b4abf7823818b93dbd18ecc0fa131c8bc75ea4cbd4d0a1e4c29d","abstract_canon_sha256":"496dd396ee99c04a2441912838ad7ef755d3a2cd94bdac24cdb89212b76d0835"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:22.049918Z","signature_b64":"SUTCx8O4yUS2WxzdqHzLyaZMbPbV9j+Irt+4psHkl8tP7be4YrElBNgJgqd7Ar17+tRW107iwl8fV9WihStnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6723f76e45ad6673b57a99fe69fef4a7463c81b4a1ae062b87d6486604e83906","last_reissued_at":"2026-05-18T00:42:22.049354Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:22.049354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite subgroups of Ham and Symp","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.SG","authors_text":"Ignasi Mundet i Riera","submitted_at":"2016-05-18T09:33:49Z","abstract_excerpt":"Let $(X,\\omega)$ be a compact symplectic manifold of dimension $2n$ and let $Ham(X,\\omega)$ be its group of Hamiltonian diffeomorphisms. 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