Block-transitive t-(k^2,k,λ) designs associated to two dimensional projective special linear groups

This paper investigates block-transitive automorphism groups of t-(k^2,k,λ) designs. Let D be a non-trivial t-(k^2,k,λ) design, G \leq \Aut(D) be block-transitive with X\unlhd G\leq \Aut(X), where X = PSL(2,q)(q\geq4). Then q = 8 and D is a 2-(36,6,λ) design with λ\in \{2,6,9,12,18,36\}.

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ArXiv.org
Published
2025-08-27
Primary Topic
Geochemistry and Geologic Mapping
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article

Block-transitive t-(k^2,k,λ) designs associated to two dimensional projective special linear groups

ArXiv.org
Geochemistry and Geologic Mapping
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Block-transitive t-(k^2,k,λ) designs associated to two dimensional projective special linear groups

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Abstract

This paper investigates block-transitive automorphism groups of t-(k^2,k,λ) designs. Let D be a non-trivial t-(k^2,k,λ) design, G \leq \Aut(D) be block-transitive with X\unlhd G\leq \Aut(X), where X = PSL(2,q)(q\geq4). Then q = 8 and D is a 2-(36,6,λ) design with λ\in \{2,6,9,12,18,36\}.

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Block-transitive t-(k^2,k,λ) designs associated to two dimensional projective special linear groups · ArXiv.org (2025) | TGRS Research Map | TGRS