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Math. Comput. Appl. 2017, 22(2), 35; doi:10.3390/mca22020035

3-Homogeneous Groups and Block-Transitive 7–(v, k, 3) Designs

Department of Mathematics Hunan, University of Humanities Science and Technology, Loudi 417000, China
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
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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-Text
Keywords: block-transitive; 3-homogeneous groups; permutation group; Affine Type Groups; Almost Simple Type Groups block-transitive; 3-homogeneous groups; permutation group; Affine Type Groups; Almost Simple Type Groups

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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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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