Is That a Polynomial?

The identity of the group doesn't swap anything but everything else has to change something. Those depend crucially on the symmetries of the original on the gal war group So you're given a set of roots is the question then What group Is there in which every element of the group preserves The polynomial but swaps the roots? Yes, okay When you say swap do you mean like maybe I'm misunderstanding or are you saying that's an example? Because when you put that in my head, I was thinking of oh like they're equidistant from the origin or something like that But if we let's say have a quartic where it just says this one so all the rationals