/sci/ - Science & Math

>>11929034
>It's better to take an extra year than to overload on courses and end up failing some because of the work load
Yeah, I know, but I'm already doing a 4 year degree in 5, so I'd be starting the Ph.D. at 24/25, which is unacceptable as we all know.

>Anyways, I would personally go with CA between the two
So CA and ODE instead of Alg Top? Any reasons? My one worry is that I decide that that's what I want to do but I have to apply for masters at the start of my senior year, so I wouldn't have done it yet.

Can anyone help me formalize a notion about permutation groups? Maybe a textbook reference for this?

Basically, starting from the symmetric group [math]S_n[/math], I want to find the smallest subgroup which is able to send every integer to every other integer (from [math]1[/math] to [math]n[/math]). So I suppose something like the subgroup [math]H < S_n[/math] such that [math]\forall i \in [n],[/math] [eqn]H(\{ i \}) = [n].[/eqn] Notation: [math][n] = \{1, \ldots, n \}[/math] and by [math]H(A)[/math] I mean the image of the usual group action of permutations on integers.

I know that the alternating group satisfies this, so my intuitive feeling is that normal subgroups might be the ingredient, but I'm not sure. I also am interested in general [math]n[/math], so the fact that e.g. [math]A_4[/math] is not simple doesn't interest me too much.