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We prove that if the nilpotence class of $U$ is less than $p$, then any embedding of $\\mathbb{G}_{a(r)}$ in $U$ lies inside a one-parameter subgroup of $U$, and there is a canonical way in which to choose such a subgroup. Applying this result, we prove that if $p$ is at least as big as the Coxeter number of $G$,"},"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":"1209.5813","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-09-26T02:05:23Z","cross_cats_sorted":[],"title_canon_sha256":"55e1c318fc67fc47eb309b18c671d070e0a80dbf17ca68f9ffafb3ec02f6df65","abstract_canon_sha256":"739719ef106377fb797a37c0ca6f0a49891d50d02df1c2ee479400c7171d35ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:46.291850Z","signature_b64":"AcYbeqAhiEiGwdcQ+o2FfdL/ePnSweLVxHqFhDjVmoB8za+G4o+ydi0fG1bbh65LMAx/x2xkMBv3vyB7TEWjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33810d66823a8a1e0ea136d77ccf2154850251e621a2f8abee452b864ec7e970","last_reissued_at":"2026-05-18T03:44:46.290392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:46.290392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On exponentiation and infinitesimal one-parameter subgroups of reductive groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Paul Sobaje","submitted_at":"2012-09-26T02:05:23Z","abstract_excerpt":"Let $G$ be a reductive algebraic group over an algebraically closed field $k$ of characteristic $p>0$, and assume $p$ is good for $G$. 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