Timeline for Smallest subgroups with trivial centralizer?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 14, 2017 at 16:40 | vote | accept | Douglas Lind | ||
| Jan 14, 2017 at 10:21 | answer | added | Alireza Abdollahi | timeline score: 4 | |
| Jan 14, 2017 at 1:55 | comment | added | Douglas Lind | In Halmos's essay How to Write Mathematics he talks about "frozen notation," asking "Who would dare write 'Let 6 be a group'?"! | |
| Jan 13, 2017 at 18:57 | comment | added | YCor | I guess there is a long list of such invariants (the smallest cardinal of a subset whose centralizer has some given smallness property etc); in a linear group one can consider the smallest cardinal of a subset generating Zariski-dense subgroup (e.g. I guess it's 2 whenever the group is not virtually solvable, and hence "$k(G)$" (I don't get used sorry, it sounds to my brain like saying "let $\mathbb{Z}$ be the field of complex numbers") would equal 2 if I'm correct. Another related object is the length of chains of centralizers (one can consider the sup, or the infimum among saturated chains). | |
| Jan 13, 2017 at 16:58 | comment | added | Douglas Lind | Yes that can mean the group ring, but I don't think there's any danger here of confusion! | |
| Jan 13, 2017 at 16:18 | comment | added | YCor | in the notation $k(G)$, usually $k$ is not a variable... but as you like! | |
| Jan 13, 2017 at 16:00 | history | asked | Douglas Lind | CC BY-SA 3.0 |