To preve this you have to assume that |X|>2.
Hi Sofia! The deadline for HW2 was yesterday. Will the deadline be extended or is this just info to help our understanding of what a correct solution would look like?
Hi,
we just wanted to point out this "degenerate case" where a group acts trivially on a set X with 2 elements a,b ( = fixing both elements). Then G = Stab(a) acts transitively on X - {a} = {b} (and same for {a}) but the action is of course not doubly transitive. This contradicts the claim of Problem 1.4 and indeed the correct argument needs at least 3 elements in X to run. But this is of course a very special and degenerate case, so if your argument is correct it will not be taken into account for the grading.
Best,
Edoardo
Hi Eduardo,
Thank you for the clarification!
Thank you for the clarification!