Timeline for Generating a finite group from elements in each conjugacy class
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 28, 2011 at 19:32 | comment | added | Geoff Robinson | The easiest example in infinite groups may be the group of invertible upper triangular matrices, which meets every conjugacy class of ${\rm GL}(n,k)$ when $k$ is an algebraically closed field. This doesn't require the full strength of the Jordan Normal Form theory. | |
| Jun 4, 2010 at 0:22 | comment | added | Noah Snyder | Very minor nitpick, you mean $(|M|-1)[G:M]+1 < |G|$ | |
| Jun 4, 2010 at 0:20 | comment | added | Noah Snyder | It's worth pointing out that this argument really uses finite. For example, for compact simple Lie groups every element lies in some torus. | |
| Jun 4, 2010 at 0:17 | comment | added | Steve D | @Kevin: there are at most $[G:M]$ conjugates of $M$, yielding at most $(|M|-1)[G:M] < |G|$ elements in $M$ and all its conjugates. | |
| Jun 4, 2010 at 0:14 | comment | added | Kevin O'Bryant | Well-known to those who know it, I suppose. What (precisely) are saying never happens? | |
| Jun 4, 2010 at 0:12 | comment | added | Steve D | "Well-known" as in "an easy exercise". | |
| Jun 4, 2010 at 0:09 | history | answered | Steve D | CC BY-SA 2.5 |