Timeline for Group cannot be the union of conjugates
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Oct 6, 2010 at 15:30 | comment | added | HJRW | Osin's example is finitely generated. Surely that's the relevant 'discreteness' criterion? (And if you think that's a minor point, try constructing a finitely presented example!) | |
| Sep 6, 2010 at 14:52 | vote | accept | C.S. | ||
| Aug 2, 2010 at 15:35 | comment | added | Torsten Ekedahl | I formulated myself badly, I do not mean that discrete should be the same as countable. I just (temporarily) wanted to make a definition of discrete that would exclude connected compact Lie groups and hence make sense of José's comment. I do think that the Osin example has a kind of discrete feel to it but of course if we should talk about just any countable group, then Robin's comment is to the point. | |
| Jul 31, 2010 at 22:29 | comment | added | Pete L. Clark | A quibble: I think this is a perfectly good "discrete" example, i.e., it uses $GL_2(\mathbb{C})$ as a group, not as a topological group. As for using "discrete" as a synonym in group theory for countable, I say boo. Consider for instance the group $\mathbb{Z}$ topologized as a subgroup of $\widehat{\mathbb{Z}}$. | |
| Jul 31, 2010 at 18:53 | comment | added | Robin Chapman | For a countable example one could just replace Keith's $\mathbb{C}$ by a countable algebraically closed field. | |
| Jul 31, 2010 at 18:47 | comment | added | Torsten Ekedahl | For a discrete (i.e., countable) example consider the example of Osin mentioned in mathoverflow.net/questions/29605/… | |
| Jul 31, 2010 at 18:21 | comment | added | José Figueroa-O'Farrill | I suppose that the OP was talking about discrete subgroups, because every element of a compact Lie group is conjugate to some maximal torus, so this sort of "infinite" is out. | |
| Jul 31, 2010 at 18:16 | history | answered | KConrad | CC BY-SA 2.5 |