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| In this paper, we study the classification offlag-transitive, point-primitive 2-(v,k,4) symmetric designs. Weprove that if the socle of the automorphism group of aflag-transitive, point-primitive nontrivial2-(v,k,4) symmetric design D is an alternating group An for n>=5, then (v,k)=(15,8) and D=(P,B) is one of the following:(i) P is the set of one-dimensional subspaces of V4(2), B is acollection of PX, where X is the set of one-dimensional subspacescontained in one hyperplane of V4(2), G=A7 or A8, andthe stabiliser Gx=L3(2) or AGL3(2) respectively.(ii) P is the set of 2- of Ω6: ={1,2,..., 6}, B is a collection ofPX, where X is Y{Y}U{Z is a 2- of Ω6 Z∩Y=θ}, Y is a 2- of Ω6, G=A6 or S6, and Gx=S4 or S4*Z2 respectively. |
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| Keywords:Group theory; Automorphism group; Alternating group |
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