Let G be a group and X be a non-empty set.

1, Can you give any definition of an action of G on X?

2, Can you give an example of a group action such that for any x in X, Stab(x) = {e} (e is the identity of G)

Problem 2 (10 points) Let G be a group and X be a non-empty set. (1) Give any definition of an action of G on X. (2) For x E X, write the definition of Stab(x), the stabilizer of x and prove that it is a subgroup of G. (3) Give an example of a group action (i.e., an explicit G, X and the action) such that V x E X, Stab(x) = {e}, where e is the identity of G