Linear constraint relations among loop-order five-point color-ordered amplitudes in $SO(N)$ and $Sp(2N)$ gauge theories are derived with the group-theoretic method. These constrains are derived up to four-loop order. It is found that in both theories, there are $n=6,22,34,44,50$ linear constraint relations at $L=0,1,2,3,4$ loop orders. Then the numbers of independent color-ordered five-point amplitudes under group-theoretic constraints are respectively $n_{ind.}=6,12,22,34,50$. We find that the number of independent color-ordered amplitudes begins to diverge from $SU(N)$ at four-loop order. This provides an evidence on the argument that group-theoretic constraint relations depend on properties of group algebras. Some comments are given on future study along this direction.

环阶五点色阶幅度之间的线性约束关系 $\mathrm{小号}Ø（ñ）$ 和 $\mathrm{小号}p（\mathrm{2个}ñ）$规范理论是通过群体理论方法得出的。这些约束可以导出到四环顺序。发现在两种理论中都有$ñ=6，22，34，44，50$ 处的线性约束关系 $\mathrm{大号}=0，\mathrm{1个}，\mathrm{2个}，3，4$循环订单。然后分别求出群理论约束下独立的有色五点幅度的个数${ñ}_{\mathrm{一世}ñd。}=6，12，22，34，50$。我们发现独立的颜色有序振幅的数量开始偏离$\mathrm{小号}ü（ñ）$在四环的顺序。这为关于群理论约束关系取决于群代数性质的论证提供了证据。沿这个方向对未来的研究提出了一些意见。