This
article is a contribution to the study of the automorphism groups of ？designs. Let be a non-trivial？？design where for some positive integer , and ？is block-transitive. If the socle of G is isomorphic to the simple groups of lie
type, then G is not flag-transitive.
References
[1]
Cameron, P.J. and Praeger, C.E. (1992) Block-Transitive t-Designs, II: Large t. In: De Clerck, F., et al., Eds., Finite geometry and Combinatorics, Deinze. (1993) London Math. Soc. Lecture Note Series, Vol. 191, Cambridge Univ. Press, Cambridge, 103-119.
Ree, R. (1961) A Family of Simple Groups Associated with the Simple Lie Algebra of Type (G2). American Journal of Mathematics, 83, 432-462. http://dx.doi.org/10.2307/2372888
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Kleidman, P.B. (1988) The Maximal Subgroups of the Chevally Groups 2G2(q) with q Odd, the Ree Groups 2G2(q), and Their Automorphism Groups. Journal of Algebra, 117, 30-71. http://dx.doi.org/10.1016/0021-8693(88)90239-6
[5]
Liu, W.J., Zhou, S., Li, H. and Fan, X. (2004) Finite Linear Spaces Admitting a Ree Simple Group. European Journal of Combinatorics, 25, 311-325. http://dx.doi.org/10.1016/j.ejc.2003.10.001
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Dai, S.J. and Zhang, R.H. (2013) The Designs with Block-Transitive Automorphism. Ars Combinatoria, 110, 15-21.
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[8]
Shen, H. (1990) The Theory of Combinatorial Design. Shanghai Jiaotong Univ. Press, Shanghai.
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