{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T06:05:35Z","timestamp":1769580335172,"version":"3.49.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,12,14]],"date-time":"2025-12-14T00:00:00Z","timestamp":1765670400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,12,14]],"date-time":"2025-12-14T00:00:00Z","timestamp":1765670400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12271173"],"award-info":[{"award-number":["12271173"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2026,1]]},"DOI":"10.1007\/s10623-025-01755-0","type":"journal-article","created":{"date-parts":[[2025,12,14]],"date-time":"2025-12-14T12:56:55Z","timestamp":1765717015000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On flag-transitive quasi-symmetric 2-designs"],"prefix":"10.1007","volume":"94","author":[{"given":"Wanbao","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Zhilin","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Shenglin","family":"Zhou","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,12,14]]},"reference":[{"issue":"2","key":"1755_CR1","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/s10623-015-0055-9","volume":"79","author":"SH Alavi","year":"2016","unstructured":"Alavi S.H., Bayat M., Daneshkhah A.: Symmetric designs admitting flag-transitive and point-primitive automorphism groups associated to two dimensional projective special groups. Des. Codes Cryptogr. 79(2), 337\u2013351 (2016).","journal-title":"Des. Codes Cryptogr."},{"issue":"3\u20134","key":"1755_CR2","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/jsco.1996.0125","volume":"24","author":"W Bosma","year":"1997","unstructured":"Bosma W., Cannon J., Playoust C.: The magma algebra system I: the user language. J. Symbol. Comput. 24(3\u20134), 235\u2013265 (1997).","journal-title":"J. Symbol. Comput."},{"key":"1755_CR3","doi-asserted-by":"crossref","unstructured":"Bray, J., Holt, D.F., Roney-Dougal, C.M.: The Maximal Subgroups of the Low-Dimensional Finite Classical Groups, With a Foreword by Martin Liebeck, London Math. Soc. Lecture Note Series, Cambridge University Press, Cambridge, Vol.\u00a0407 (2013).","DOI":"10.1017\/CBO9781139192576"},{"key":"1755_CR4","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1016\/0097-3165(88)90056-8","volume":"49","author":"F Buekenhout","year":"1988","unstructured":"Buekenhout F., Delandtsheer A., Doyen J.: Finite linear spaces with flag-transitive group. J. Combin. Theory Ser. A 49, 268\u2013293 (1988).","journal-title":"J. Combin. Theory Ser. A"},{"key":"1755_CR5","first-page":"89","volume":"36","author":"F Buekenhout","year":"1990","unstructured":"Buekenhout F., Delandtsheer A., Doyen J., Kleidman P.B., Liebeck M.W., Saxl J.: Linear spaces with flag-transitive automorphism groups. Geom. Dedicata 36, 89\u201394 (1990).","journal-title":"Geom. Dedicata"},{"key":"1755_CR6","series-title":"Discrete Mathematics and Its Applications","volume-title":"Handbook of Combinatorial Designs","author":"CJ Colburn","year":"2007","unstructured":"Colburn C.J., Dinitz J.H.: Handbook of Combinatorial Designs, 2nd edn Discrete Mathematics and Its Applications. Chapman & Hall\/CRC, Boca Raton (2007).","edition":"2"},{"key":"1755_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-62012-6","volume-title":"Finite Geometries","author":"P Dembowski","year":"1968","unstructured":"Dembowski P.: Finite Geometries. Springer, New York (1968)."},{"key":"1755_CR8","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1016\/j.jcta.2015.01.002","volume":"132","author":"A Devillers","year":"2015","unstructured":"Devillers A., Praeger C.E.: Pairwise transitive 2-designs. J. Combin. Theory Ser. A 132, 246\u2013270 (2015).","journal-title":"J. Combin. Theory Ser. A"},{"issue":"4","key":"1755_CR9","doi-asserted-by":"publisher","first-page":"1041","DOI":"10.5802\/alco.297","volume":"6","author":"A Devillers","year":"2023","unstructured":"Devillers A., Praeger C.E.: Analysing flag-transitive point-imprimitive $$2$$-designs. Algebr. Combin. 6(4), 1041\u20131055 (2023).","journal-title":"Algebr. Combin."},{"key":"1755_CR10","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/0012-365X(87)90154-3","volume":"63","author":"H Davies","year":"1987","unstructured":"Davies H.: Flag-transitivity and primitivity. Discrete Math. 63, 91\u201393 (1987).","journal-title":"Discrete Math."},{"key":"1755_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0731-3","volume-title":"Permutation Groups","author":"JD Dixon","year":"1996","unstructured":"Dixon J.D., Mortimer B.: Permutation Groups. Springer, New York (1996)."},{"key":"1755_CR12","unstructured":"The GAP Group.: GAP-Groups, Algorithms, and Programming, Version 4.8.4 (2017). http:\/\/www.gap-system.org"},{"key":"1755_CR13","unstructured":"Giudici, M.: Maximal subgroups of almost simple groups with socle $$PSL(2,q)$$, Manuscript, arxiv.org\/abs\/math\/0703685v1 (2007)."},{"issue":"1","key":"1755_CR14","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/0021-8693(87)90019-6","volume":"106","author":"WM Kantor","year":"1987","unstructured":"Kantor W.M.: Primitive permutation groups of odd degree, and an application to finite projective planes. J. Algebra 106(1), 15\u201345 (1987).","journal-title":"J. Algebra"},{"issue":"5","key":"1755_CR15","doi-asserted-by":"publisher","first-page":"1009","DOI":"10.1016\/j.jcta.2008.12.005","volume":"116","author":"M Law","year":"2009","unstructured":"Law M., Praeger C.E., Reichard S.: Flag-transitive symmetric 2-(96,20,4) designs. J. Combin. Theory Ser. A 116(5), 1009\u20131022 (2009).","journal-title":"J. Combin. Theory Ser. A"},{"key":"1755_CR16","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1017\/S144678870003216X","volume":"44","author":"MW Liebeck","year":"1988","unstructured":"Liebeck M.W., Praeger C.E., Saxl J.: On the O\u2019Nan-Scott theorem for finite primitive permutation groups. J. Austral. Math. Soc. 44, 389\u2013396 (1988).","journal-title":"J. Austral. Math. Soc."},{"issue":"5","key":"1755_CR17","doi-asserted-by":"publisher","first-page":"114398","DOI":"10.1016\/j.disc.2025.114398","volume":"348","author":"JB Lu","year":"2025","unstructured":"Lu J.B., Zhuang Y.: Flag-transitive point-primitive 2-designs with block intersection numbers $$0$$ and $$y\\le 10$$. Discrete Math. 348(5), 114398 (2025).","journal-title":"Discrete Math."},{"key":"1755_CR18","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/s10623-023-01307-4","volume":"92","author":"ZW Lu","year":"2024","unstructured":"Lu Z.W., Zhou S.L.: Flag-transitive symmetric 2-designs of prime order. Des. Codes Cryptogr. 92, 259\u2013266 (2024).","journal-title":"Des. Codes Cryptogr."},{"key":"1755_CR19","doi-asserted-by":"crossref","unstructured":"Mandi\u00b4c, J., \u0160uba\u0161i\u00b4c, A.: Flag-transitive and point-imprimitive symmetric designs with $$\\lambda \\le 10$$, J. Combin. Theory Ser. A 189, 105620 (2022).","DOI":"10.1016\/j.jcta.2022.105620"},{"key":"1755_CR20","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1007\/BF01194419","volume":"52","author":"VC Mavron","year":"1989","unstructured":"Mavron V.C., Shrikhande M.S.: Designs with intersection numbers 0 and 2. Arch. Math. 52, 407\u2013412 (1989).","journal-title":"Arch. Math."},{"issue":"6","key":"1755_CR21","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1002\/jcd.3180030607","volume":"3","author":"TP McDonough","year":"1995","unstructured":"McDonough T.P., Mavron V.C.: Quasi-symmetric designs with good blocks. J. Combin. Des. 3(6), 433\u2013441 (1995).","journal-title":"J. Combin. Des."},{"key":"1755_CR22","doi-asserted-by":"crossref","unstructured":"Neumaier, A.: Regular sets and quasi-symmetric 2-designs. In: Combinatorial Theory (Schloss Rauischholzhausen, 1982). In: Lecture Notes in Mathematics. Springer, vol.\u00a0969, 258\u2013275 (1982)","DOI":"10.1007\/BFb0062999"},{"issue":"2","key":"1755_CR23","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1112\/jlms\/s2-47.2.227","volume":"47","author":"CE Praeger","year":"1993","unstructured":"Praeger C.E.: An O\u2019Nan-Scott theorem for finite quasi-primitive permutation groups and an application to 2-arc transitive graphs. J. Lond. Math. Soc. 47(2), 227\u2013239 (1993).","journal-title":"J. Lond. Math. Soc."},{"issue":"1","key":"1755_CR24","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1016\/S0021-8693(03)00400-9","volume":"269","author":"CE Praeger","year":"2003","unstructured":"Praeger C.E.: Quotients and inclusions of finite quasi-primitive permutation groups. J. Algebra 269(1), 329\u2013346 (2003).","journal-title":"J. Algebra"},{"key":"1755_CR25","doi-asserted-by":"crossref","unstructured":"Praeger, C.E.: Finite quasi-primitive graphs, in: Surveys in Combinatorics, (London), in: London Math. Soc. Lecture Notes Ser., 241, 65-85, (1997).","DOI":"10.1017\/CBO9780511662119.005"},{"key":"1755_CR26","doi-asserted-by":"crossref","unstructured":"Praeger, C.E., Schneider, C.: Permutation groups and Cartesian decompositions. London Mathematics Society. Lecture Note Series, Cambridge University Press, Cambridge 449, (2018).","DOI":"10.1017\/9781139194006"},{"key":"1755_CR27","doi-asserted-by":"crossref","unstructured":"Praeger, C.E., Zhou, S.L.: Imprimitive flag-transitive symmetric designs. J. Combin. Theory Ser. A 113(7), 1381\u20131395 (2006)","DOI":"10.1016\/j.jcta.2005.12.006"},{"issue":"2","key":"1755_CR28","first-page":"127","volume":"36","author":"DL Tian","year":"2016","unstructured":"Tian D.L., Zhou S.L.: Classification of flag-transitive primitive symmetric $$(v, k, \\lambda )$$ designs with $${\\rm PSL}(2, q)$$ as socle. J. Math. Res. Appl. 36(2), 127\u2013139 (2016).","journal-title":"J. Math. Res. Appl."},{"issue":"4","key":"1755_CR29","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1002\/jcd.21337","volume":"21","author":"DL Tian","year":"2013","unstructured":"Tian D.L., Zhou S.L.: Flag-transitive point-primitive symmetric $$(v, k, \\lambda )$$ designs with $$\\lambda $$ at most 100. J. Comb. Des. 21(4), 127\u2013141 (2013).","journal-title":"J. Comb. Des."},{"key":"1755_CR30","doi-asserted-by":"crossref","unstructured":"Shrikhande, Y.M.S., Sane, S.S.: Quasi-symmetric designs, London Math. Soc. Lecture Note Ser., 164 Cambridge University Press, Cambridge, (1991), xvi+225 pp.","DOI":"10.1017\/CBO9780511665615"},{"key":"1755_CR31","doi-asserted-by":"crossref","unstructured":"Rotman, J.J.: An introduction to the theory of groups, 4th edition, Graduate Texts in Mathematics (Vol.\u00a0148). Springer, New York (1995). xvi+513 pp.","DOI":"10.1007\/978-1-4612-4176-8"},{"issue":"4","key":"1755_CR32","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/S0195-6698(13)80137-0","volume":"11","author":"IA Farad\u017eev","year":"1990","unstructured":"Farad\u017eev I.A., Ivanov A.A.: Distance-transitive representations of groups $$G$$ with $${\\rm PSL}(2, q) \\unlhd G \\le {\\rm P\\Gamma L}(2, q)$$. Eur. J. Combin. 11(4), 347\u2013356 (1990).","journal-title":"Eur. J. Combin."},{"key":"1755_CR33","doi-asserted-by":"publisher","first-page":"2765","DOI":"10.1007\/s10623-018-0474-5","volume":"86","author":"XQ Zhan","year":"2018","unstructured":"Zhan X.Q., Zhou S.L.: Non-symmetric 2-designs admitting a two-dimensional projective linear group. Des. Codes Cryptogr. 86, 2765\u20132773 (2018).","journal-title":"Des. Codes Cryptogr."},{"key":"1755_CR34","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1002\/jcd.21924","volume":"32","author":"ZL Zhang","year":"2024","unstructured":"Zhang Z.L., Chen J.F., Zhou S.L.: On symmetric designs with flag-transitive and point-quasiprimitive automorphism groups. J. Combin. Des. 32, 107\u2013126 (2024).","journal-title":"J. Combin. Des."},{"key":"1755_CR35","doi-asserted-by":"crossref","unstructured":"Zhang, W.B., Zhou, S.L.: Flag-transitive quasi-symmetric designs with block intersection numbers 0 and 2, 22(4), 2350093 (2023).","DOI":"10.1142\/S0219498823500937"},{"key":"1755_CR36","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1016\/0021-8693(88)90027-0","volume":"118","author":"PH Zieschang","year":"1988","unstructured":"Zieschang P.H.: Flag-transitive automorphism groups of $$2$$-designs with $$(r,\\lambda )=1$$. J. Algebra 118, 369\u2013375 (1988).","journal-title":"J. Algebra"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-025-01755-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-025-01755-0","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-025-01755-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,26]],"date-time":"2026-01-26T17:13:02Z","timestamp":1769447582000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-025-01755-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,14]]},"references-count":36,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["1755"],"URL":"https:\/\/doi.org\/10.1007\/s10623-025-01755-0","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,14]]},"assertion":[{"value":"19 February 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 October 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 November 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 December 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"4"}}