We find the lower central series for residually nilpotent Baumslag-Solitar groups, and find the intersection of all terms of the lower central series. Also, we find non-abelian Bauslag-Solitar groups for which the lower central series has length 2. For some Baumslag-Solitar groups a connection is found between the intersection of all subgroups of finite index and the intersection of all terms of the lower central series.

中文翻译：

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Baumslag-Solitar 群的下中央系列

我们找到剩余幂零 Baumslag-Solitar 群的下中心级数，并找到下中心级数的所有项的交集。此外，我们发现了非阿贝尔 Bauslag-Solitar 群，其下中心级数的长度为 2。对于一些 Baumslag-Solitar 群，在有限索引的所有子群的交集与下中心级的所有项的交集之间找到了联系系列。