Sporadic simple groups as flag-transitive automorphism groups of symmetric designs

Seyed Hassan Alavi; Ashraf Daneshkhah

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arXiv · 2307.05184

Sporadic simple groups as flag-transitive automorphism groups of symmetric designs

Seyed Hassan Alavi·Ashraf Daneshkhah

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Abstract

In this article, we study symmetric designs admitting flag-transitive, point-imprimitive almost simple automorphism groups with socle sporadic simple groups. As a corollary, we present a classification of symmetric designs admitting flag-transitive automorphism group whose socle is a sporadic simple group, and in conclusion, there are exactly seven such designs, one of which admits a point-imprimitive automorphism group and the remaining are point-primitive.

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Seyed Hassan Alavi, Ashraf Daneshkhah. 2023-07-11. Sporadic simple groups as flag-transitive automorphism groups of symmetric designs. https://arxiv.org/abs/2307.05184

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