Exercise
Consider G = S5 acting on the subsets of size 2 of {1,2,3,4,5}. Which of the sequences below is a basis?
[{1,2}, {3,4}]
[{1,2}, {3,4}, {3,5}]
[{1,2}, {1,3}, {1,4}]
[{1,2}, {1,3}, {2,3}, {4,5}]
No.
The element (1,2) stabilizes both {1,2} and {3,4}.
No.
The element (1,2) stabilizes all three.
Yes.
No.
The permutation (4,5) stabilizes each element.