Timeline for Commutator subgroup of rotational symmetries of the hypercube
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 18, 2015 at 3:07 | review | Close votes | |||
| Aug 18, 2015 at 5:38 | |||||
| Aug 9, 2015 at 19:45 | comment | added | Derek Holt | @IgorRivin I wasn't claiming it was obvious! The permutation module for $S_n$ over any field has exactly two nonzero proper submodules, of dimensions $1$ and $n-1$. That is a known result. My claim above follows from this (together with $[S_n,S_n]=A_n$), but I wouldn't describe it as obvious. If the characteristic of the field divides $n$ then the smaller submodule is contained in the larger submodule - otherwise they are disjoint. | |
| Aug 9, 2015 at 15:43 | comment | added | Igor Rivin | @DerekHolt This is obvious for $n$ odd, but is it also obvious for $n$ even? | |
| Aug 9, 2015 at 15:02 | comment | added | Derek Holt | For $n \ge 3$, the commutator subgroup is the subgroup of index $2$ consisting of those elements in which $\sigma$ is even. This subgroup is perfect for $n \ge 5$. | |
| Aug 9, 2015 at 13:07 | review | Close votes | |||
| Aug 10, 2015 at 10:05 | |||||
| Aug 9, 2015 at 9:58 | review | First posts | |||
| Aug 9, 2015 at 10:56 | |||||
| Aug 9, 2015 at 9:55 | history | asked | quelramodellago | CC BY-SA 3.0 |