Bulletin of the Belgian Mathematical Society - Simon Stevin

Flag-transitive point-primitive non-symmetric $2$-$(v,k,2)$ designs with alternating socle

Hongxue Liang and Shenglin Zhou

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We prove that if $\mathcal{D}$ is a non-trivial non-symmetric $2$-$(v,k,2)$ design admitting a flag-transitive point-primitive automorphism group $G$ with $Soc(G)=A_{n}$ for $n\geq5$, then $\mathcal{D}$ is a $2$-$(6,3,2)$ or $2$-$(10,4,2)$ design.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 23, Number 4 (2016), 559-571.

First available in Project Euclid: 6 December 2016

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Primary: 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX] 05B05: Block designs [See also 51E05, 62K10] 20B15: Primitive groups

primitive group flag-transitive; non-symmetric design alternating socle


Liang, Hongxue; Zhou, Shenglin. Flag-transitive point-primitive non-symmetric $2$-$(v,k,2)$ designs with alternating socle. Bull. Belg. Math. Soc. Simon Stevin 23 (2016), no. 4, 559--571. doi:10.36045/bbms/1480993587. https://projecteuclid.org/euclid.bbms/1480993587

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