Timeline for The automorphisms of a 2-group of nilpotency class 2
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 11, 2013 at 11:47 | comment | added | BHZ | I am really thankful for your help and your very useful comments. | |
| Apr 11, 2013 at 11:09 | comment | added | Derek Holt | In any nilpotent group of class 2, we have $[ab,c]=[a,c][b,c]$ and $[a,b]^{-1} =[b,a]$, so the commutator map is bilinear and alternating, and we get an induced map $G/Z(G) \times G/Z(G) \to Z(G)$. If $|Z(G)|=2$, then $[a^2,b]=1$ for all $a,b$, so $a^2 \in Z(G)$ and $G/Z(G)$ is elementary abelian. So $G$ is extraspecial. | |
| Apr 11, 2013 at 9:27 | comment | added | BHZ | Excuse me, the commutator map is from $G/Z(G)\times G/Z(G)$ to $G/Z(G)$ or $Z(G)$? I am sorry, since I am not fammilar with these subjects. | |
| Apr 11, 2013 at 9:04 | comment | added | BHZ | Thank you very much for your kindness and your helps. Could you kindly introduce me some references for these subjects for example why $k$ is odd and why $G/Z(G)$ must be elementary abelian. | |
| Apr 11, 2013 at 8:57 | vote | accept | BHZ | ||
| Apr 11, 2013 at 8:55 | history | answered | Derek Holt | CC BY-SA 3.0 |