Flag-transitive 2-\upsilon ,\mathrm{5},\lambda designs with sporadic socle

Abstract

We state that the ag-transitive automorphism group of a 2-\upsilon ,\mathrm{5},\lambda design \mathcal{D} is primitive of affine type or almost simple type. We also find that there are up to isomorphism 20 2-\upsilon ,\mathrm{5},\lambda designs admitting flag-transitive automorphism groups with socle of a sporadic simple group.

Key words： 2-design; primitivity; flag-transitivity; sporadic simple group

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