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Designs, Codes and Cryptography

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01-12-2016

Flag-transitive non-symmetric 2-designs with \((r,\lambda )=1\) and sporadic socle

Authors: Xiaoqin Zhan, Shenglin Zhou

Published in: Designs, Codes and Cryptography | Issue 3/2016

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Abstract

This paper is a contribution to the investigation of flag-transitive non-symmetric 2-designs. We prove that if \({\mathcal {D}}\) is a non-trivial non-symmetric 2-\((v,k,\lambda )\) design with \((r,\lambda )=1\) and \(G\le Aut({\mathcal {D}})\) is flag-transitive with sporadic socle, then \({\mathcal {D}}\) must be one of following: a 2-(12, 6, 5) design with \(G=M_{11}\), or a 2-(22, 6, 5) design with \(G=M_{22}\) or \(M_{22}:2\).

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Title: Flag-transitive non-symmetric 2-designs with and sporadic socle
Authors: Xiaoqin Zhan
Shenglin Zhou
Publication date: 01-12-2016
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 3/2016
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-015-0171-6

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Flag-transitive non-symmetric 2-designs with \((r,\lambda )=1\) and sporadic socle

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