Timeline for Quotient of subgroups by center.

13 events

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May 20, 2011 at 3:01	comment	added	Arturo Magidin		@Stuart: If $N\triangleleft G$ and $H$ is any subgroup of $G$, then $(H\cap N)\triangleleft H$, because $hNh^{-1}=N$ and $hHh^{-1}=H$ for all $h\in H$.
May 19, 2011 at 17:57	vote	accept	Stuart
May 19, 2011 at 17:51	comment	added	Stuart		Umm... yeah, clearly because if it is in the center it commutes with everything... thanks again!
May 19, 2011 at 17:47	comment	added	Stuart		So if I follow correctly, because of that, it follows that ($H \cap Z_G$) is normal in $H$ because it is a subgroup of the center?
May 19, 2011 at 17:42	vote	accept	Stuart
May 19, 2011 at 17:45
May 19, 2011 at 17:42	comment	added	Stuart		I didnt realize $Z_H \geq (H \cap Z_G)$. Then that means that $HZ_G/Z_G$ is actually a subgroup and everything is fine. Thanks!!
May 19, 2011 at 17:38	comment	added	Arturo Magidin		@Stuart: Oh, I see what the problem was; a typo. I meant "the third term of the lower central series of $F_k$; fixed.
May 19, 2011 at 17:38	history	edited	Arturo Magidin	CC BY-SA 3.0	typo
May 19, 2011 at 17:37	vote	accept	Stuart
May 19, 2011 at 17:38
May 19, 2011 at 17:31	history	edited	Arturo Magidin	CC BY-SA 3.0	added 311 characters in body; added 9 characters in body
May 19, 2011 at 17:28	comment	added	Stuart		If G is nilpotent of class 2, then the third term of the lower central series is trivial, is it not?
May 19, 2011 at 17:25	history	edited	Arturo Magidin	CC BY-SA 3.0	added 334 characters in body
May 19, 2011 at 17:16	history	answered	Arturo Magidin	CC BY-SA 3.0