It is shown that, apart from the smallest Ree group, a flag-transitive automorphism group G of a 2-(k^2, 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-(6^2, 6, 2) design or to one of the three 2- (6^2, 6, 6) designs constructed in this paper. All the four 2-designs have the 36 secants of a non-degenerate conic C of PG(2,8) as a point set and 6-sets of secants in a remarkable configuration as a block set.

On flag-transitive 2-(k^2, k, λ) designs with λ | k

Alessandro Montinaro
;
Eliana Francot
2022-01-01

Abstract

It is shown that, apart from the smallest Ree group, a flag-transitive automorphism group G of a 2-(k^2, 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-(6^2, 6, 2) design or to one of the three 2- (6^2, 6, 6) designs constructed in this paper. All the four 2-designs have the 36 secants of a non-degenerate conic C of PG(2,8) as a point set and 6-sets of secants in a remarkable configuration as a block set.
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Note: Creative Commons 4.0 International Link to Publisher version: https://onlinelibrary.wiley.com/doi/10.1002/jcd.21852 Citation: Montinaro, A., and Francot, E., On flag-transitive 2- designs with , J Combin Des. (2022), 30, 653– 670
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11587/479546
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