Math. Comput. Appl. 2017, 22(2), 35; doi:10.3390/mca22020035
3-Homogeneous Groups and Block-Transitive 7–(v, k, 3) Designs
1
Department of Mathematics Hunan, University of Humanities Science and Technology, Loudi 417000, China
2
School of Mathematics and Statistics, Changshu Institute of Technology, Changshu 215500, China
*
Author to whom correspondence should be addressed.
Academic Editor: Fazal M. Mahomed
Received: 25 November 2016 / Revised: 25 May 2017 / Accepted: 29 May 2017 / Published: 15 June 2017
Abstract
The classification of a block-transitive designs is an important subject on algebraic combinatorics. With the aid of MATLAB software, using the classification theorem of 3-homogeneous permutation groups, we look at the classification problem of block-transitive 7–(v, k, 3) design and prove our main theorem: If the automorphism group of a 7–(v, k, 3) design is block-transitive, then it is neither isomorphic to Affine Type Groups nor Almost Simple Type Groups. View Full-TextKeywords:
block-transitive; 3-homogeneous groups; permutation group; Affine Type Groups; Almost Simple Type Groups
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Liao, X.; Chen, G.; Li, S. 3-Homogeneous Groups and Block-Transitive 7–(v, k, 3) Designs. Math. Comput. Appl. 2017, 22, 35.
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