{"title":"On flag‐transitive 2‐ (k2,k,λ) $({k}^{2},k,lambda )$ designs with λ∣k $lambda | k$","authors":"Alessandro Montinaro, Eliana Francot","doi":"10.1002/jcd.21852","DOIUrl":"https://doi.org/10.1002/jcd.21852","url":null,"abstract":"It is shown that, apart from the smallest Ree group, a flag‐transitive automorphism group G $G$ of a 2‐ (k2,k,λ) $({k}^{2},k,lambda )$ design D ${mathscr{D}}$ , with λ∣k $lambda | k$ , is either an affine group or an almost simple classical group. Moreover, when G $G$ is the smallest Ree group, D ${mathscr{D}}$ is isomorphic either to the 2‐ (62,6,2) $({6}^{2},6,2)$ design or to one of the three 2‐ (62,6,6) $({6}^{2},6,6)$ designs constructed in this paper. All the four 2‐designs have the 36 secants of a non‐degenerate conic C ${mathscr{C}}$ of PG2(8) $P{G}_{2}(8)$ as a point set and 6‐sets of secants in a remarkable configuration as a block set.","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"20 1","pages":"653 - 670"},"PeriodicalIF":0.7,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76703413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}