{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T03:41:32Z","timestamp":1776397292415,"version":"3.51.2"},"reference-count":14,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T00:00:00Z","timestamp":1736208000000},"content-version":"vor","delay-in-days":6,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871181"],"award-info":[{"award-number":["11871181"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>\n                    In this paper, the problem of unipotency for the matrix group generated by two matrices is examined. By employing matrix logarithms as a tool, various combinatorial formulas for matrices were derived by selecting different primitive elements. Key conclusions were then reached through the organization and simplification of these formulas. It was ultimately demonstrated, based on these conclusions, that a matrix group\n                    <jats:italic>G<\/jats:italic>\n                    generated by two matrices, where the Jordan blocks do not exceed third order, must be unipotent if each primitive element of\n                    <jats:italic>G<\/jats:italic>\n                    is unipotent and has an order of six or less.\n                  <\/jats:p>","DOI":"10.1155\/2025\/1423635","type":"journal-article","created":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T04:50:09Z","timestamp":1736225409000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Unipotency of Matrix Group Generated by Two Matrices"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-4681-4298","authenticated-orcid":false,"given":"Yanshuo","family":"Cheng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3944-1079","authenticated-orcid":false,"given":"Xinsong","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,1,7]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-3685-3"},{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.6040\/j.issn.1671-9352.0.2022.555"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498823501530"},{"key":"e_1_2_7_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2024.03.008"},{"key":"e_1_2_7_5_2","first-page":"1","article-title":"Power zero supergroup [J\/OL]","author":"Chi Z.","year":"2024","journal-title":"Science China Mathematics"},{"key":"e_1_2_7_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/s41980-024-00883-y"},{"key":"e_1_2_7_7_2","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.2000.8413"},{"key":"e_1_2_7_8_2","first-page":"66","article-title":"Wreath products structure of super R\u2217-unipotent semigroups","volume":"44","author":"Xiaomin Z.","year":"2009","journal-title":"Journal of Shandong University"},{"key":"e_1_2_7_9_2","doi-asserted-by":"publisher","DOI":"10.19492\/j.cnki.1672-0946.2012.04.023"},{"key":"e_1_2_7_10_2","volume-title":"Linear representation of the power unity of the free group of dimension 9","author":"Xin D.","year":"2021"},{"key":"e_1_2_7_11_2","volume-title":"Power-similarity of a free group with linear representation dimension 9","author":"Xin D.","year":"2021"},{"key":"e_1_2_7_12_2","volume-title":"The power single condition of the group of binary generator matrix","author":"Jiaxin L.","year":"2022"},{"key":"e_1_2_7_13_2","doi-asserted-by":"publisher","DOI":"10.15938\/j.jhust.2021.06.019"},{"key":"e_1_2_7_14_2","volume-title":"Unipotency of free group generated by two elements of linearly represent with any dimensionality","author":"Chaoran Z.","year":"2021"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2025\/1423635","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/2025\/1423635","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2025\/1423635","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T02:43:18Z","timestamp":1776393798000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2025\/1423635"}},"subtitle":[],"editor":[{"given":"Kamal","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1155\/2025\/1423635"],"URL":"https:\/\/doi.org\/10.1155\/2025\/1423635","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1]]},"assertion":[{"value":"2024-03-29","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-10-04","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-01-07","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"1423635"}}