2 gen corner permutation

[Lykos]

Hello,

I heard doing corner permutation with 2-gen algorithms on 2x2 is impossible. When I try it out, it seems intuitively impossible to permute corners of the top layer while preserving the bottom layer using 2-gen algs. But I still don't really see why. The fact that edge orientation with a 2 gen alg is impossible is easy to understand, but for corner permutation, I don't really get it yet. Can anyone explain me? Is there any invariant that is preserved by every turn and that stops the corners from being permuted or something like that?

 

[guysensei1]

On a 2x2, perform (R U)*7 R

You've permuted 2 corners

 

[shadowslice e]

This page is pretty good
Essentially, there are three groups you can have for 6 corners which are reachable using {R, U} generators within each group but only 1 group contains the solved state. The Briggs method has a method of transforming each to the Solvable group but is not exactly easy to recognise quickly.
The solvable group only has one other CP case in it: Adj/Opp