%0 Journal Article
%T Block-Transitive 4-(<i>v</i>,<i>k</i>,4) Designs  and Ree Groups
%A Shaojun Dai
%A Ruihai Zhang
%J Advances in Pure Mathematics
%P 317-320
%@ 2160-0384
%D 2016
%I Scientific Research Publishing
%R 10.4236/apm.2016.65022
%X This
article is a contribution to the study of the automorphism groups of <img src=\"Edit_dd060fb7-1df4-4146-8eae-3c2c54eec228.bmp\" alt=\"\" /><span lang=\"EN-US\">&nbsp;designs. Let <img src=\"Edit_eb447014-7e04-4eed-a9f4-77e962f6ca4a.bmp\" alt=\"\" /></span><span lang=\"EN-US\">be a non-trivial&nbsp;<img src=\"Edit_3a6b181c-cb1c-4140-a8e2-da5798077ebc.bmp\" alt=\"\" /></span><span lang=\"EN-US\">&nbsp;design where <img src=\"Edit_18022808-ce17-4e5a-9028-61bb610f4669.bmp\" alt=\"\" /></span><span lang=\"EN-US\">for some positive integer <img src=\"Edit_b77ac337-b876-48e8-8ba5-5fc20043ec7c.bmp\" alt=\"\" /></span><span lang=\"EN-US\">, and <img src=\"Edit_0c78e20b-0e89-46f2-b4a2-23bb8d43ab91.bmp\" alt=\"\" /></span><span lang=\"EN-US\">&nbsp;is block-transitive. If the socle of <i>G</i> is isomorphic to the simple groups of lie
type<img src=\"Edit_f30e136b-e6ae-4815-bd9e-6e61a2b40599.bmp\" alt=\"\" /></span><span lang=\"EN-US\">, then <i>G</i> is not flag-transitive.</span>
%K Flag-Transitive
%K Block-Transitive
%K t-Design
%K Ree Group
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=65362