Journal article

On flag-transitive 2-(v, k, 2) designs

Alice Devillers, Hongxue Liang, Cheryl E Praeger, Binzhou Xia

JOURNAL OF COMBINATORIAL THEORY SERIES A | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2021

Abstract

This paper is devoted to the classification of flag-transitive 2-(v,k,2) designs. We show that apart from two known symmetric 2-(16,6,2) designs, every flag-transitive subgroup G of the automorphism group of a nontrivial 2-(v,k,2) design is primitive of affine or almost simple type. Moreover, we classify the 2-(v,k,2) designs admitting a flag transitive almost simple group G with socle PSL(n,q) for some n≥3. Alongside this analysis we give a construction for a flag-transitive 2-(v,k−1,k−2) design from a given flag-transitive 2-(v,k,1) design which induces a 2-transitive action on a line. Taking the design of points and lines of the projective space PG(n−1,3) as input to this construction yie..

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University of Melbourne Researchers

Grants

Awarded by Australian Research Council


Awarded by Guangdong Basic and Applied Basic Research Foundation


Funding Acknowledgements

The first and third author were supported by the Australian Research Council Discovery Project DP200100080. The second author's work on this paper was done when she was visiting the University of Western Australia, and forms part of her dissertation for the PhD of South China University of Technology supervised by Prof. Shenglin Zhou. She is grateful to the School of Mathematics and Statistics at the University of Western Australia for hospitality in 2017 when she did the main work on this paper, and to Guangdong Basic and Applied Basic Research Foundation (No. 2019A1515110908) and South China University of Technology for financial support. The fourth author's work on this paper was done when he was a research associate at the University of Western Australia supported by the Australian Research Council Discovery Project DP150101066. The authors would like to thank the anonymous referees for their valuable suggestions.