Flag-transitive 2-(v, k, λ) symmetric designs with (k, λ) = 1 and alternating socle

Abstract

Consider the flag-transitive 2-(v, k, λ) symmetric designs with (k, λ) = 1. We prove that if {D} is a nontrivial 2-(v, k, λ) symmetric design with (k, λ) = 1 and G≤Aut({D}) is flag-transitive with Soc(G) = A_n for n≥5, then {D} is the projective space PG₂(3,2) and G = A₇.

Keywords

Symmetric design / automorphism group / alternating group / flagtransitive

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