关于三维Projective Geometries参数的Abel差集
On Abelian Difference Sets with Parameters of 3-dimensional Projective Geometries
摘要：
如果$ (v,k, λ) = (\frac{q^d-1}{q-1}, \frac{q^{d-1}-1}{q-1}, \frac{q^{d-2}-1}{q-1}).$这种情况$d=3$对应于平面差集，则称差集具有经典参数。本文主要研究具有$d=4$的阿贝尔差集族。这种差集的唯一已知例子对应于射影几何$PG(3,q)$。我们考虑一个任意差集的参数$PG(3,q)$在一个阿贝尔群和建立限制其结构。特别是，我们辨别嵌入的子结构。
英文摘要：
A difference set is said to have classical parameters if $ (v,k, λ) = (\frac{q^d-1}{q-1}, \frac{q^{d-1}-1}{q-1}, \frac{q^{d-2}-1}{q-1}).$ The case $d=3$ corresponds to planar difference sets. We focus here on the family of abelian difference sets with $d=4$. The only known examples of such difference sets correspond to the projective geometries $PG(3,q)$. We consider an arbitrary difference set with the parameters of $PG(3,q)$ in an abelian group and establish constraints on its structure. In particular, we discern embedded substructures.
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