/sci/ - Science & Math

>>12740178
Darling, everything is just an array of numbers.

>>12739308
Good heavens, based!

>>12738853
>the number of orbits/whatever other property isn’t invariant under choice of group action
Obviously not. If you take the usual left action, then there is only one orbit, but the trivial action makes every orbit a singleton. One thing I thought of quickly was to ask which subgroups would stay fixed under this action. Say you knew that all normal subgroups are precisely your fixed subgroups. This would mean that your action should be conjugation. Similarly, having no fixed subgroups other than the group itself would suggest translation, every subgroup the trivial action and so on. Maybe up to some equivalence relation, these would let you map your set of fixed subgroups to the (class represented by) the action that would keep precisely those fixed. However, this could fail if you could find a set of subgroups that would not correspond to any action at all, and I'm only thinking about finite groups. Just some random and quick ideas, maybe (probably) total rubbish.

>>12565824
Good, you haven't completely changed. I must admit I don't know enough of those things to make any interesting or even content filled comment, but it's nice to see you didn't abandon your main thing even if AdS went to the trash can.

>>12207237
Same but 3 weeks. I tell mine of all the stupid ideas I had and was unable to take to the end or turned out to be stupid after checking the details.