对称1-设计从PGL2(q)，为奇数素数幂

Pub Date : 2021-06-24 DOI:10.3336/gm.56.1.01

Xavier Mbaale, B. Rodrigues

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引用次数: 1

摘要

确定了所有的非平凡点和块基元1-(v, k, k)设计，它们允许群G = PGL2(q)，其中q是一个奇素数的幂，作为自同构的置换群。这些自对偶和对称的1-设计是通过定义{|M|/|M∩Mg|: g∈g}为g在M共轭上的原元作用的轨道长度的集合来构造的。

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Symmetric 1-designs from PGL2(q), for q an odd prime power

All non-trivial point and block-primitive 1-(v, k, k) designs 𝓓 that admit the group G = PGL2(q), where q is a power of an odd prime, as a permutation group of automorphisms are determined. These self-dual and symmetric 1-designs are constructed by defining { |M|/|M ∩ Mg|: g ∈ G } to be the set of orbit lengths of the primitive action of G on the conjugates of M.

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