{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:GI3PBAHSYJJDPSPNGBFZ4B3DVE","short_pith_number":"pith:GI3PBAHS","schema_version":"1.0","canonical_sha256":"3236f080f2c25237c9ed304b9e0763a939826ba6830ed58896d37ea6c8aa6a6d","source":{"kind":"arxiv","id":"1403.2057","version":2},"attestation_state":"computed","paper":{"title":"Generation of finite classical groups by pairs of elements with large fixed point spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"\\'Akos Seress, Cheryl E. Praeger, \\c{S}\\\"ukr\\\"u Yal\\c{c}inkaya","submitted_at":"2014-03-09T13:46:12Z","abstract_excerpt":"We study `good elements' in finite $2n$-dimensional classical groups $G$: namely $t$ is a `good element' if $o(t)$ is divisible by a primitive prime divisor of $q^n-1$ for the relevant field order $q$, and $t$ fixes pointwise an $n$-space. The group ${\\rm{SL}}_{2n}(q)$ contains such elements, and they are present in ${\\rm{Su}}_{2n}(q), {\\rm{Sp}}_{2n}(q), {\\rm{So}}^\\epsilon_{2n}(q)$, only if $n$ is odd, even, even, respectively. We prove that there is an absolute positive constant $c$ such that two random conjugates of $t$ generate $G$ with probability at least $c$, if $G\\ne {\\rm{Sp}}_{2n}(q)$ "},"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":"1403.2057","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-03-09T13:46:12Z","cross_cats_sorted":[],"title_canon_sha256":"44055b8d9f30d83fb08682cf3512e42b7a3127142ae7429d86108b1bf48948f3","abstract_canon_sha256":"9d7695e26b554a60bb2f35f6f344fc7af64e9b6eef757526f558ad5d441c2afa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:23.139393Z","signature_b64":"yhUpTjz0YmR4YxsCaE6WBossZMBX/ZiTcOs00NJpkwCvreL0mNSzbTD2VXfDbatm1aKCYFxE3e6cVe/bPOK6Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3236f080f2c25237c9ed304b9e0763a939826ba6830ed58896d37ea6c8aa6a6d","last_reissued_at":"2026-05-18T02:52:23.138421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:23.138421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generation of finite classical groups by pairs of elements with large fixed point spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"\\'Akos Seress, Cheryl E. Praeger, \\c{S}\\\"ukr\\\"u Yal\\c{c}inkaya","submitted_at":"2014-03-09T13:46:12Z","abstract_excerpt":"We study `good elements' in finite $2n$-dimensional classical groups $G$: namely $t$ is a `good element' if $o(t)$ is divisible by a primitive prime divisor of $q^n-1$ for the relevant field order $q$, and $t$ fixes pointwise an $n$-space. The group ${\\rm{SL}}_{2n}(q)$ contains such elements, and they are present in ${\\rm{Su}}_{2n}(q), {\\rm{Sp}}_{2n}(q), {\\rm{So}}^\\epsilon_{2n}(q)$, only if $n$ is odd, even, even, respectively. We prove that there is an absolute positive constant $c$ such that two random conjugates of $t$ generate $G$ with probability at least $c$, if $G\\ne {\\rm{Sp}}_{2n}(q)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2057","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1403.2057","created_at":"2026-05-18T02:52:23.138760+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.2057v2","created_at":"2026-05-18T02:52:23.138760+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2057","created_at":"2026-05-18T02:52:23.138760+00:00"},{"alias_kind":"pith_short_12","alias_value":"GI3PBAHSYJJD","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"GI3PBAHSYJJDPSPN","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"GI3PBAHS","created_at":"2026-05-18T12:28:30.664211+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GI3PBAHSYJJDPSPNGBFZ4B3DVE","json":"https://pith.science/pith/GI3PBAHSYJJDPSPNGBFZ4B3DVE.json","graph_json":"https://pith.science/api/pith-number/GI3PBAHSYJJDPSPNGBFZ4B3DVE/graph.json","events_json":"https://pith.science/api/pith-number/GI3PBAHSYJJDPSPNGBFZ4B3DVE/events.json","paper":"https://pith.science/paper/GI3PBAHS"},"agent_actions":{"view_html":"https://pith.science/pith/GI3PBAHSYJJDPSPNGBFZ4B3DVE","download_json":"https://pith.science/pith/GI3PBAHSYJJDPSPNGBFZ4B3DVE.json","view_paper":"https://pith.science/paper/GI3PBAHS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.2057&json=true","fetch_graph":"https://pith.science/api/pith-number/GI3PBAHSYJJDPSPNGBFZ4B3DVE/graph.json","fetch_events":"https://pith.science/api/pith-number/GI3PBAHSYJJDPSPNGBFZ4B3DVE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GI3PBAHSYJJDPSPNGBFZ4B3DVE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GI3PBAHSYJJDPSPNGBFZ4B3DVE/action/storage_attestation","attest_author":"https://pith.science/pith/GI3PBAHSYJJDPSPNGBFZ4B3DVE/action/author_attestation","sign_citation":"https://pith.science/pith/GI3PBAHSYJJDPSPNGBFZ4B3DVE/action/citation_signature","submit_replication":"https://pith.science/pith/GI3PBAHSYJJDPSPNGBFZ4B3DVE/action/replication_record"}},"created_at":"2026-05-18T02:52:23.138760+00:00","updated_at":"2026-05-18T02:52:23.138760+00:00"}