Let G be a generalized Baumslag–Solitar group, and let $\mathcal{C}$ be a class of groups containing at least one non-trivial group and closed under taking subgroups, extensions, and Cartesian products of the form ${\prod }_{y\in Y}{X}_y$, where X, $Y\in \mathcal{C}$ and $X_y$ is an isomorphic copy of X for every $y\in Y$. We give a criterion for G to be residually a $\mathcal{C}$-group provided $\mathcal{C}$ consists only of periodic groups. We also prove that G is residually a torsion-free $\mathcal{C}$-group if $\mathcal{C}$ contains at least one non-periodic group and is closed under taking homomorphic images. These facts generalize and strengthen some known results. We also provide criteria for a GBS-group to be a) residually nilpotent; b) residually torsion-free nilpotent; c) residually free.

令G为广义Baumslag–Solitar群，令$\mathcal{C}$ 是一类包含至少一个非平凡组的组，并在形式为的子组，扩展和笛卡尔乘积下封闭 ${\prod }_{ÿ\in ÿ}{X}_{ÿ}$，其中X，$ÿ\in \mathcal{C}$ 和 $X_{ÿ}$是每个X的同构副本$ÿ\in ÿ$。我们给出一个准则，使G残差为a$\mathcal{C}$-组提供 $\mathcal{C}$仅由周期性组组成。我们还证明G完全没有扭转$\mathcal{C}$-如果 $\mathcal{C}$包含至少一个非周期组，并在拍摄同态图像时关闭。这些事实概括并加强了一些已知的结果。我们还为GBS组提供了以下标准：a）剩余幂等；b）残余无扭力的零能；c）残余自由。