二维典型群PSL(2,q)与旗传递2-(v, k, λ)设计

doi:10.16088/j.issn.1001-6600.2017.02.006

Abstract

Abstract: Flag-transitivity is one of the many conditions that can be imposed on the automorphism group G of a 2-(v,k,λ) design D. In 1988, it is proved by Zieschang that if D is a 2-(v,k,λ) design, G≤Aut(G) is flag-transitive and (r,λ)=1, then G is affine or almost simple. So it is possible to classify this type of designs by using the classification of finite simple groups. Let D be a nontrivial 2-(v,k,λ) design with (r,λ)=1 and v≤1 000, and let G≤Aut(D) be flag-transitive with Soc(G)PSL(2,q). It is proved that, up to isomorphism, there are exactly 18 pairs (D, G).

Key words: 2-design, flag-transitive, point-primitive, socle, two dimensional classical groups

CLC Number:

O152.1

WANG Pei, ZHOU Shenglin. Two Dimensional Classical Groups PSL(2,q)and Flag-transitive 2-(v,k,λ) Designs[J].Journal of Guangxi Normal University(Natural Science Edition), 2017, 35(2): 39-44.

References

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Two Dimensional Classical Groups PSL(2,q)and Flag-transitive 2-(v,k,λ) Designs

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