Section 1 gives a brief review of known results on embeddings of solvable, nilpotent, and polycyclic groups in 2-generated groups from these classes, including the description of the author’s recently obtained solution to the Mikaelian–Ol’schanskii problem on embeddings of finitely generated solvable groups of derived length l in solvable groups of derived length l + 1 with a fixed small number of generators.

Section 2 contains a somewhat more extensive review of known results on the rational subset membership problem for groups, including the presentation of the author’s recently obtained solution to the Laurie–Steinberg–Kambites–Silva–Zetsche problem of whether the membership problem is decidable for finitely generated submonoids of free nilpotent groups.

第1节简要概述了这些类别中2个生成的组中可溶，幂零和多环基团的嵌入的已知结果，包括作者最近获得的关于有限生成的Mikaelian–Ol'schanskii问题的解的描述。带有固定数量的生成器的派生长度为l + 1的可解组中的派生长度为l的可解组。

第2节包含有关组的有理子集成员资格问题的已知结果的更广泛的综述，包括作者最近获得的关于劳氏–斯坦伯格–坎比特斯–席尔瓦–泽切问题的解决方案，关于成员资格是否可以确定的问题产生自由幂零基团的亚类生物。