this is a wonderful thing you have done. You have a way of making the rigorous mathematics approachable, not by reducing the rigour, but by explaining every step. Great job. It helped me.
I think I finally have it. Grossly, Auto(G) is set of all set permutations of a larger Symmetric Group S_G , that when acted on elements of G, will map isomorphically to the elements of G. It's like Normalizers of Symmetric Group S_G where the Set is the GroupG. And by the proofs above it obeys 4 laws of group axioms , and thus is a subgroup of S_G. The Inn(G) are sets of all set permutations but within G, that maps G to G isomorphically. Again it also obeys 4 axioms of group theory , thus is a subgroup of Auto(G). By inspection Inn(G) is also a subgroup of G.
this is a wonderful thing you have done. You have a way of making the rigorous mathematics approachable, not by reducing the rigour, but by explaining every step. Great job. It helped me.
Thank you very much for your videos, it helps me a lot!
By set permutation, do you mean coset?
I think I finally have it. Grossly, Auto(G) is set of all set permutations of a larger Symmetric Group S_G , that when acted on elements of G, will map isomorphically to the elements of G. It's like Normalizers of Symmetric Group S_G where the Set is the GroupG.
And by the proofs above it obeys 4 laws of group axioms , and thus is a subgroup of S_G.
The Inn(G) are sets of all set permutations but within G, that maps G to G isomorphically. Again it also obeys 4 axioms of group theory , thus is a subgroup of Auto(G). By inspection Inn(G) is also a subgroup of G.