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(2) If $G$ is a connected affine Nash group, then there exist a largest toroidal affine Nash subgroup $\\ant{G}$ and a largest connected, normal, almost linear affine Nash subgroup $\\aff{G}$. Moreover, we have $G=\\ant{G}\\aff{G}$, and $\\ant{G}\\cap \\aff{G}$ "},"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":"1509.06687","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-22T17:13:06Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"e928c90d9818f336a9dee239ae8c1500a4800dbab277402eebcf8f6e852e1c06","abstract_canon_sha256":"e04d7c3d8671477f96f928623208a82eeeca3436cb4ffa14cf932a639e4e3e60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:32.910773Z","signature_b64":"zBMVXQAzQg+DeTWbOUNHmRdSEcy9hOEl7C+iAIuM7feBwMVybnsG47Y7LIVJsOFEy105xZiZTf1J1YCprenoAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"698cd242c7e1446b2d41cf343a62457a9f8383dac38565e9b972daea40398e8a","last_reissued_at":"2026-05-18T01:17:32.910042Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:32.910042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Toroidal affine Nash groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Mahir Bilen Can","submitted_at":"2015-09-22T17:13:06Z","abstract_excerpt":"A toroidal affine Nash group is the affine Nash group analogue of an anti-affine algebraic group. In this note, we prove analogues of Rosenlicht's structure and decomposition theorems: (1) Every affine Nash group $G$ has a smallest normal affine Nash subgroup $H$ such that $G/H$ is an almost linear affine Nash group, and this $H$ is toroidal. (2) If $G$ is a connected affine Nash group, then there exist a largest toroidal affine Nash subgroup $\\ant{G}$ and a largest connected, normal, almost linear affine Nash subgroup $\\aff{G}$. 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