Timeline for Given any group G, how can we construct another group H such that G is isomorphic to the commutator subgroup H' of H?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Aug 29, 2018 at 18:58 | comment | added | Alireza Abdollahi | See the following post mathoverflow.net/questions/85540/… | |
| Aug 24, 2018 at 20:00 | comment | added | YCor | @verret I agree it's broad but disagree that it's the same as asking the commutator subgroup of every finite group... for instance say for the group $G=C_2$, the question makes sense and does not reduce in such a tautological way. The answer then starts with $H=P\times A$ where $A$ is abelian of odd order and $P$ is a 2-group with derived subgroup $C_2$. Then the description of such 2-groups is a reasonable question. The OP should maybe specify what (s)he did so far. | |
| Aug 23, 2018 at 22:01 | review | Close votes | |||
| Aug 28, 2018 at 3:05 | |||||
| Aug 23, 2018 at 21:42 | comment | added | verret | How is the second question different from asking for the commutator subgroup of every finite group? I think this is way too broad. | |
| Aug 23, 2018 at 16:53 | comment | added | Geoff Robinson | I think any semidirect product $H.A$ with $A$ an Abelian group of automorphisms of $H$ acting trivially on $H/H^{\prime}$ will also have derived group $H^{\prime}.$ | |
| Aug 23, 2018 at 16:36 | comment | added | Praphulla Koushik | Abstract concept can come from random thought (which still needs proof but not in the beginning)... if you are asking for all groups having some property you better have one example of a group where you have that property.. My comment is also random thought :D | |
| Aug 23, 2018 at 16:34 | comment | added | YCor | @Dey you can rather prove it as an exercise: what is the derived subgroup of $G\wr C_2=(G\times G)\rtimes C_2$ (action by flip), for $G$ abelian? | |
| Aug 23, 2018 at 16:32 | comment | added | Dey | @Geoff Thanks for this information. Didn't know this result! Can you please provide some reference where I can find the proof? | |
| Aug 23, 2018 at 16:30 | comment | added | Dey | @Praphulla Random thought! | |
| Aug 23, 2018 at 16:26 | comment | added | Geoff Robinson | I suppose you know that any finite Abelian group $G$ is isomorphic to $H^{\prime},$ where $H = G \wr \left( \mathbb{Z}/2\mathbb{Z} \right).$ Probably OK for infinite Abelian groups too. | |
| Aug 23, 2018 at 16:24 | comment | added | Praphulla Koushik | What is your motivation for the question.. just out of curiosity I am asking... | |
| Aug 23, 2018 at 16:17 | history | asked | Dey | CC BY-SA 4.0 |