Timeline for Being a subgroup: proof by character theory
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Nov 5, 2011 at 18:10 | comment | added | Steve D | Perhaps he means you are just given the character table of some group $G$, and you know nothing else about it: can you list (some of) the subgroups, and to what extent? I take his comment to be a generalization of the well-known fact that one can read off normal subgroups from the character table. | |
| Nov 5, 2011 at 17:53 | comment | added | Johannes Hahn | @Will: That would be equally trivial. The only groups that don't have proper nontrivial subgroups are the groups of prime order. Those groups are of course very, very easy to recognize by their character table. I think John mac though in his comment (it isn't really an answer) more about specific types of subgroups. Questions like "Does there exists a centralizer of an involution that has properties X and Y but not property Z" are very interesting and it would certainly be an achievement if one were able to provide a general answer in terms of the character table. | |
| Nov 5, 2011 at 16:12 | comment | added | Will Sawin | Presumably, he meant a proper nontrivial subgroup? | |
| Nov 5, 2011 at 15:40 | comment | added | GH from MO | Trivially, every group has a subgroup $H$, e.g. $H=G$. So I am not sure what you wanted to say. | |
| Nov 5, 2011 at 13:21 | history | answered | John mac | CC BY-SA 3.0 |