On Flag-Transitive 2-(k², k, λ) Designs with λ| k

2022/03/17 by Alessandro Montinaro, Montinaro, Alessandro, Eliana Francot +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2203.09254

openalex publication_date 2022/03/17 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

It is shown that, apart from the smallest Ree group, a flag-transitive automorphism group G of a 2-(k², k, λ) design D, with λ| k, is either an affine group or an almost simple classical group. Moreover, when G is the smallest Ree group, D is isomorphic either to the 2-(62, 6, 2) design or to one of the three 2- (62, 6, 6) designs constructed in this paper. All the four 2-designs have the 36 secants of a nondegenerate conic C of PG₂(8) as a point set and 6-sets of secants in a remarkable configuration as a block set.

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