Timeline for Comparing lower central series and augmentation ideal completions
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 12, 2010 at 13:25 | comment | added | Simon Wadsley | I think that all these things will be true when $G^p$ is profinite (in fact necessarily pro-$p$ in that case). Moreover $G$ finitely generated will suffice for this. I suggest consulting a book on profinite or pro-$p$ books such as those by J.S. Wilson or Dixon, Du Sautoy, Mann and Segal. | |
| Sep 12, 2010 at 8:14 | comment | added | user2529 | Is the group $G\gamma_qG$ nilpotent for arbitrary group $G$? I think if $G$ is nilpotent, then $\varprojlim_{q}{\mathbb{Z}}/p[G]/I^q$ is isomorphic to $\varprojlim_{q}{\mathbb{Z}}/p[G/\gamma_qG]$. Am I right? any comments are welcome. thanks | |
| Sep 11, 2010 at 9:46 | comment | added | Simon Wadsley | I think Torsten has now basically answered that question. Probably never yes for infinite groups but you can say something. | |
| Sep 11, 2010 at 0:32 | comment | added | user2529 | First, thank you for your answer and the reference.:) Then I correct mistake of $\gamma_qG$. In the case of $G$ not abelian group, with what conditions (such as finitely generated not abel group) the answer will be Yes? | |
| Sep 10, 2010 at 16:22 | comment | added | Simon Wadsley | I should perhaps add that these $I$-adically completed things are studied mostly under the name of Iwasawa algebras. See math.uiuc.edu/documenta/vol-coates/ardakov_brown.html for a survey of algebraic results. | |
| Sep 10, 2010 at 14:43 | history | answered | Simon Wadsley | CC BY-SA 2.5 |