论文标题
有限生成的残留nilpotent组的nilpotent属
The nilpotent genus of finitely generated residually nilpotent groups
论文作者
论文摘要
如果$ g $和$ h $是有限生成的剩余nilpotent群体，则$ g $和$ h $在同一nilpotent属中，如果它们具有相同的较低的中心持有人（直至同构）。一个更强的条件是，如果存在$ g $ $ g $的$ h $中的$ h $是$ g $，这会引起其下中央系列的相应商之间的同构。我们首先考虑剩余的小组，并在单态性上找到足够的条件，以便$ h $是para-$g。$ $我们然后证明，对于某些polycyclic群体，如果$ h $是para-$ g $，则$ g $，$ g $，$ h $具有相同的hirsch长度。我们还证明，这些多环类的促态完成是局部多环状的。
If $G$ and $H$ are finitely generated residually nilpotent groups, then $G$ and $H$ are in the same nilpotent genus if they have the same lower central quotients (up to isomorphism). A stronger condition is that $H$ is para-$G$ if there exists a monomorphism of $G$ into $H$ which induces isomorphisms between the corresponding quotients of their lower central series. We first consider residually nilpotent groups and find sufficient conditions on the monomorphism so that $H$ is para-$G.$ We then prove that for certain polycyclic groups, if $H$ is para-$G$, then $G$ and $H$ have the same Hirsch length. We also prove that the pro-nilpotent completions of these polycyclic groups are locally polycyclic.
