TY - JOUR T1 - BLOCK TRANSITIVE 2 − (v, 17, 1) DESIGNS AND REE GROUPS AU - Dai, Shaojun AU - Zhao, Kun PY - 2012 DA - December JF - International Electronic Journal of Algebra JO - IEJA PB - Abdullah HARMANCI WT - DergiPark SN - 1306-6048 SP - 12 EP - 16 VL - 12 IS - 12 LA - en AB - This article is a contribution to the study of the automorphism groups of 2 − (v, k, 1) designs. Let D be 2 − (v, 17, 1) design, G ≤ Aut(D) be block transitive and point primitive. If G is unsolvable, then Soc(G), the socle of G, is not 2G2(q). KW - block transitive KW - design KW - Ree groups CR - F. Buekenhout, A. Delandtsheer, J. Doyen, P. Kleidman, M. W. Liebeck and J. Saxl, Linear spaces with flag transitive automorphism groups, Geom. Dedicata, (1990), 89-94. CR - P. C. Calpham, Steiner system with block transitive automorphism groups, Discrete Math., 14 (1976), 121-131. CR - A. Camina and J. Siemons, Block-transitive automorphism groups of (v, k, 1) design, J. Comb. Theory A, 51 (1989), 268-276. CR - G. G. Han and H. L. Li, Unsolvable block transitive automorphism groups of − (v, 5, 1) designs, J. Comb. Theory A, 114 (2007),77-96. CR - G. G. Han and C. G. Ma, Block transitive 2 − (v, 11, 1) design and classical simple groups, Adv Math., 39 (3)(2010), 319-330. CR - P. B. Kleidman, The maximal subgroups of the Chevally groups2G2(q) with q odd, the Ree groups2G2(q), and their automorphism groups, J. Algebra, 117 (1988), 30-71. CR - H. Li, On block-transitive 2 − (v, 4, 1) designs, J. Combin. Theory Ser. A, 69 (1995), 115-124. CR - M. Liebeck and J. Saxl, On the orders of maximal subgroups of the finite exceptional groups of Lie type, Proc. Lond. Math. Soc., 55 (1987), 299-330. CR - W. J. Liu, Block transitive 2 − (v, k, 1) designs, Ph.D. Thesis, Zhejiang Uni- versity, 1998. CR - R. Ree, A family of simple groups associated with the simple Lie algebra of type (G2), Amer. J. Math., 83 (1961), 432-462. CR - W. Tong and H. L. Li, Solvable block transitive automorphism groups of 2 − (v, 5, 1) designs, Discrete Math., 260 (2003), 267-273. Shaojun Dai CR - Department of Mathematics Tianjin Polytechnic University No. 399 Binshuixi Road, Xiqing District Tianjin, P.R.China e-mail: daishaojun@tjpu.edu.cn Kun Zhao School of Science, Jiamusi University Jiamusi, Heilongjiang, P.R.China e-mail: zhaokun197808@126.com UR - https://dergipark.org.tr/en/pub/ieja/issue//266269 L1 - https://dergipark.org.tr/en/download/article-file/232792 ER -